Question
A coordinate graph shows a positive slope, in quadrant 4 there are dotted numbers (0, -4), and (1, -1)
Using the graph, derive the equation of the line in slope-intercept form.
(1 point)
Responses
3x−y=4
3 x minus y equals 4
y=−3x−4
y equals negative 3 x minus 4
y=3x−4
y equals 3 x minus 4
y=3x+4
Using the graph, derive the equation of the line in slope-intercept form.
(1 point)
Responses
3x−y=4
3 x minus y equals 4
y=−3x−4
y equals negative 3 x minus 4
y=3x−4
y equals 3 x minus 4
y=3x+4
Answers
Answer
Another coordinate graph shows a negative slope in the 4th quadrant there is a dotted number (1, -4), and in the y axis there is another dotted number (0, 1)
Write the equation of the line in slope-intercept form.
(1 point)
Responses
y=5x+1
y equals 5 x plus 1
−5x−y=−1
negative 5 x minus y equals negative 1
y=−5x−1
y equals negative 5 x minus 1
y=−5x+1
y equals negative 5 x plus 1
Write the equation of the line in slope-intercept form.
(1 point)
Responses
y=5x+1
y equals 5 x plus 1
−5x−y=−1
negative 5 x minus y equals negative 1
y=−5x−1
y equals negative 5 x minus 1
y=−5x+1
y equals negative 5 x plus 1
Answer
Graph the linear equation y=−3x+2.
Answer
A coordinate graph is shown with a negative slope, a dotted number lies on the y axis (0, 3), and another one in quadrant one (3, 2)
Is this the correct graph of y=−1/3x+4 ?(1 point)
Responses
No, it is not the correct graph because this graph has a positive slope.
No, it is not the correct graph because this graph has a positive slope.
Yes, it is the correct graph because this graph has a y-intercept of (0,3).
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis .
Yes, it is the correct graph because this graph has a y-intercept of (0,4).
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .
No, it is not the correct graph because this graph used (0,3) as the y-intercept.
Is this the correct graph of y=−1/3x+4 ?(1 point)
Responses
No, it is not the correct graph because this graph has a positive slope.
No, it is not the correct graph because this graph has a positive slope.
Yes, it is the correct graph because this graph has a y-intercept of (0,3).
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis .
Yes, it is the correct graph because this graph has a y-intercept of (0,4).
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .
No, it is not the correct graph because this graph used (0,3) as the y-intercept.
Answer
Graph the linear equation
y=2/3x−1 .
y=2/3x−1 .
Answer
# of mules Bales of hay
2 1
4 2
6 3
8 4
10 5
and a graph is shown where it costs 30 dollars for 20 square feet of carpet
a. The slope for the bales of hay and mules is Response area
b. The slope for cost and square footage of carpet is Response area
c. Which situation has the greatest rate of change?
2 1
4 2
6 3
8 4
10 5
and a graph is shown where it costs 30 dollars for 20 square feet of carpet
a. The slope for the bales of hay and mules is Response area
b. The slope for cost and square footage of carpet is Response area
c. Which situation has the greatest rate of change?
Answered by
Just_Natsume
The options for part B is 2 15 2 5 30 2/3 3/2 10
Answered by
Just_Natsume
A coordinate graph show a positive slope the first dotted numbers resting on the y axis (0, 4) and the second set of numbers in the first quadrant as (1, 8)
Derive the equation of the line in slope-intercept form.
Derive the equation of the line in slope-intercept form.
Answered by
Just_Natsume
another coordinate graph shows a negative slope the first dotted numbers laying on the y axis as (0, 2) the second dotted number in the fourth quadrant as (1, -1)
Write the equation of the line in slope-intercept form.
Write the equation of the line in slope-intercept form.
Answered by
Just_Natsume
Another coordinate graph shows a positive slope with the first set of dotted numbers on the y axis as (0, -2), and the second set of numbers resting on the x axis as (3, 0)
Write the equation of the line in slope-intercept form.
Write the equation of the line in slope-intercept form.
Answered by
Just_Natsume
Given the equation y=−2x+2 , what is the slope? Write your answer as an integer.(1 point)
The slope is (BLANK).
The slope is (BLANK).
Answered by
Just_Natsume
Given the equation y=3/4x−2 what is the y -intercept? Write your answer as an ordered pair.(1 point)
The y-intercept is ((BLANK)).
The y-intercept is ((BLANK)).
Answered by
GPT-4o mini
To derive the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) using the coordinates given.
The two points provided are (0, -4) and (1, -1).
1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3
\]
2. **Now that we have the slope (m = 3)**, we can use one of the points to find the y-intercept (b). Let's use the point (0, -4):
\[
y = mx + b
\]
Plugging in the point (0, -4):
\[
-4 = 3(0) + b \\
-4 = b
\]
3. **Now we have everything needed for the equation**:
\[
y = 3x - 4
\]
Thus, the correct answer is:
**y = 3x - 4**
The two points provided are (0, -4) and (1, -1).
1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3
\]
2. **Now that we have the slope (m = 3)**, we can use one of the points to find the y-intercept (b). Let's use the point (0, -4):
\[
y = mx + b
\]
Plugging in the point (0, -4):
\[
-4 = 3(0) + b \\
-4 = b
\]
3. **Now we have everything needed for the equation**:
\[
y = 3x - 4
\]
Thus, the correct answer is:
**y = 3x - 4**
Answered by
GPT-4o mini
To find the equation of the line in slope-intercept form (y = mx + b), we first determine the slope (m) using the two points provided: (1, -4) and (0, 1).
1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-4)}{0 - 1} = \frac{1 + 4}{-1} = \frac{5}{-1} = -5
\]
2. **Now that we have the slope (m = -5)**, we can use one of the points to find the y-intercept (b). We can use the point (0, 1):
\[
y = mx + b
\]
Plugging in the point (0, 1):
\[
1 = -5(0) + b \\
1 = b
\]
3. **Now we have everything needed for the equation**:
\[
y = -5x + 1
\]
Thus, the correct answer is:
**y = -5x + 1**.
1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-4)}{0 - 1} = \frac{1 + 4}{-1} = \frac{5}{-1} = -5
\]
2. **Now that we have the slope (m = -5)**, we can use one of the points to find the y-intercept (b). We can use the point (0, 1):
\[
y = mx + b
\]
Plugging in the point (0, 1):
\[
1 = -5(0) + b \\
1 = b
\]
3. **Now we have everything needed for the equation**:
\[
y = -5x + 1
\]
Thus, the correct answer is:
**y = -5x + 1**.
Answered by
GPT-4o mini
To graph the linear equation \( y = -3x + 2 \), follow these steps:
### Step 1: Identify the slope and y-intercept
The equation is in slope-intercept form \( y = mx + b \), where:
- \( m \) (slope) = -3
- \( b \) (y-intercept) = 2
This means the line crosses the y-axis at (0, 2).
### Step 2: Plot the y-intercept
Start by plotting the y-intercept on the graph:
- Point (0, 2).
### Step 3: Use the slope to find another point
The slope of -3 can also be written as \(-3/1\). This means that for every 1 unit you move to the right (positive x-direction), you move down 3 units (negative y-direction).
From the point (0, 2):
1. Move 1 unit to the right: \( x = 1 \).
2. Move down 3 units: \( y = 2 - 3 = -1 \).
Now you have another point (1, -1) that you can plot.
### Step 4: Plot the second point
Plot the second point:
- Point (1, -1).
### Step 5: Draw the line
Now that you have the points (0, 2) and (1, -1) plotted, draw a straight line through these points, extending it in both directions.
### Step 6: Label (optional)
You may label the equation of the line on the graph as \( y = -3x + 2 \) for clarity.
This is how you would graph the equation \( y = -3x + 2 \). If you are using graphing software or a graphing calculator, you can input the equation directly to see the line and its characteristics visually represented.
### Step 1: Identify the slope and y-intercept
The equation is in slope-intercept form \( y = mx + b \), where:
- \( m \) (slope) = -3
- \( b \) (y-intercept) = 2
This means the line crosses the y-axis at (0, 2).
### Step 2: Plot the y-intercept
Start by plotting the y-intercept on the graph:
- Point (0, 2).
### Step 3: Use the slope to find another point
The slope of -3 can also be written as \(-3/1\). This means that for every 1 unit you move to the right (positive x-direction), you move down 3 units (negative y-direction).
From the point (0, 2):
1. Move 1 unit to the right: \( x = 1 \).
2. Move down 3 units: \( y = 2 - 3 = -1 \).
Now you have another point (1, -1) that you can plot.
### Step 4: Plot the second point
Plot the second point:
- Point (1, -1).
### Step 5: Draw the line
Now that you have the points (0, 2) and (1, -1) plotted, draw a straight line through these points, extending it in both directions.
### Step 6: Label (optional)
You may label the equation of the line on the graph as \( y = -3x + 2 \) for clarity.
This is how you would graph the equation \( y = -3x + 2 \). If you are using graphing software or a graphing calculator, you can input the equation directly to see the line and its characteristics visually represented.
Answered by
GPT-4o mini
To determine if the graph corresponds to the equation \( y = -\frac{1}{3}x + 4 \), we need to evaluate the slope and y-intercept.
1. **Identify the y-intercept**:
- The given equation \( y = -\frac{1}{3}x + 4 \) has a y-intercept of (0, 4).
- The given graph has a y-intercept of (0, 3).
2. **Identify the slope**:
- The slope of the line is \(-\frac{1}{3}\), indicating a negative slope (the line decreases as it moves from left to right).
- The graph mentioned has a negative slope, which matches the slope of the equation.
Since the graph shows a y-intercept of (0, 3), which does not match the y-intercept of 4 from the equation, we can conclude the following:
**The correct response is:**
No, it is not the correct graph because this graph used (0, 3) as the y-intercept.
1. **Identify the y-intercept**:
- The given equation \( y = -\frac{1}{3}x + 4 \) has a y-intercept of (0, 4).
- The given graph has a y-intercept of (0, 3).
2. **Identify the slope**:
- The slope of the line is \(-\frac{1}{3}\), indicating a negative slope (the line decreases as it moves from left to right).
- The graph mentioned has a negative slope, which matches the slope of the equation.
Since the graph shows a y-intercept of (0, 3), which does not match the y-intercept of 4 from the equation, we can conclude the following:
**The correct response is:**
No, it is not the correct graph because this graph used (0, 3) as the y-intercept.
Answered by
GPT-4o mini
To graph the linear equation \( y = \frac{2}{3}x - 1 \), follow these steps:
### Step 1: Identify the slope and y-intercept
The equation is in slope-intercept form \( y = mx + b \), where:
- \( m \) (slope) = \( \frac{2}{3} \)
- \( b \) (y-intercept) = -1
This means the line crosses the y-axis at the point (0, -1).
### Step 2: Plot the y-intercept
Start by plotting the y-intercept on the graph:
- Point (0, -1).
### Step 3: Use the slope to find another point
The slope of \( \frac{2}{3} \) means that for every 3 units you move to the right (positive x-direction), you move up 2 units (positive y-direction).
From the point (0, -1):
1. Move 3 units to the right: \( x = 3 \).
2. Move 2 units up: \( y = -1 + 2 = 1 \).
Now you have another point (3, 1) that you can plot.
### Step 4: Plot the second point
Plot the second point:
- Point (3, 1).
### Step 5: Draw the line
Now that you have plotted the points (0, -1) and (3, 1), draw a straight line through these points, extending it in both directions.
### Step 6: Label the line (optional)
You may label the equation of the line on the graph as \( y = \frac{2}{3}x - 1 \) for clarity.
### Summary of Points
1. First point: (0, -1) (y-intercept)
2. Second point: (3, 1)
This provides a clear representation of the graph for the equation \( y = \frac{2}{3}x - 1 \). If you are using graphing software or a graphing calculator, you can input the equation directly to visualize the line.
### Step 1: Identify the slope and y-intercept
The equation is in slope-intercept form \( y = mx + b \), where:
- \( m \) (slope) = \( \frac{2}{3} \)
- \( b \) (y-intercept) = -1
This means the line crosses the y-axis at the point (0, -1).
### Step 2: Plot the y-intercept
Start by plotting the y-intercept on the graph:
- Point (0, -1).
### Step 3: Use the slope to find another point
The slope of \( \frac{2}{3} \) means that for every 3 units you move to the right (positive x-direction), you move up 2 units (positive y-direction).
From the point (0, -1):
1. Move 3 units to the right: \( x = 3 \).
2. Move 2 units up: \( y = -1 + 2 = 1 \).
Now you have another point (3, 1) that you can plot.
### Step 4: Plot the second point
Plot the second point:
- Point (3, 1).
### Step 5: Draw the line
Now that you have plotted the points (0, -1) and (3, 1), draw a straight line through these points, extending it in both directions.
### Step 6: Label the line (optional)
You may label the equation of the line on the graph as \( y = \frac{2}{3}x - 1 \) for clarity.
### Summary of Points
1. First point: (0, -1) (y-intercept)
2. Second point: (3, 1)
This provides a clear representation of the graph for the equation \( y = \frac{2}{3}x - 1 \). If you are using graphing software or a graphing calculator, you can input the equation directly to visualize the line.
Answered by
GPT-4o mini
To find the slope for both situations described, we will use the formula for slope, given two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
### a. The slope for the bales of hay and mules
The data provided is:
- 2 mules yield 1 bale of hay
- 4 mules yield 2 bales of hay
- 6 mules yield 3 bales of hay
- 8 mules yield 4 bales of hay
- 10 mules yield 5 bales of hay
We can use any two points from the data for our calculation. Let’s use the first two points:
When:
- \( (2, 1) \) and \( (4, 2) \)
Calculating the slope:
\[
\text{slope} = \frac{2 - 1}{4 - 2} = \frac{1}{2}
\]
### Response for part a:
**The slope for the bales of hay and mules is \( \frac{1}{2} \).**
### b. The slope for cost and square footage of carpet
You mentioned that it costs $30 for 20 square feet of carpet. This gives us one point of interest: \( (20, 30) \).
If we consider a standard situation like \( (0, 0) \):
We could also find out how much it costs per square foot.
Calculating the slope using points \( (0, 0) \) and \( (20, 30) \):
\[
\text{slope} = \frac{30 - 0}{20 - 0} = \frac{30}{20} = \frac{3}{2} = 1.5
\]
### Response for part b:
**The slope for cost and square footage of carpet is \( 1.5 \).**
### c. Which situation has the greatest rate of change?
To compare the slopes:
- Rate of change for bales of hay and mules: \( \frac{1}{2} = 0.5 \)
- Rate of change for cost and square footage of carpet: \( 1.5 \)
Since \( 1.5 \) is greater than \( 0.5 \), we can conclude:
### Response for part c:
**The situation with the greatest rate of change is the cost and square footage of carpet.**
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
### a. The slope for the bales of hay and mules
The data provided is:
- 2 mules yield 1 bale of hay
- 4 mules yield 2 bales of hay
- 6 mules yield 3 bales of hay
- 8 mules yield 4 bales of hay
- 10 mules yield 5 bales of hay
We can use any two points from the data for our calculation. Let’s use the first two points:
When:
- \( (2, 1) \) and \( (4, 2) \)
Calculating the slope:
\[
\text{slope} = \frac{2 - 1}{4 - 2} = \frac{1}{2}
\]
### Response for part a:
**The slope for the bales of hay and mules is \( \frac{1}{2} \).**
### b. The slope for cost and square footage of carpet
You mentioned that it costs $30 for 20 square feet of carpet. This gives us one point of interest: \( (20, 30) \).
If we consider a standard situation like \( (0, 0) \):
We could also find out how much it costs per square foot.
Calculating the slope using points \( (0, 0) \) and \( (20, 30) \):
\[
\text{slope} = \frac{30 - 0}{20 - 0} = \frac{30}{20} = \frac{3}{2} = 1.5
\]
### Response for part b:
**The slope for cost and square footage of carpet is \( 1.5 \).**
### c. Which situation has the greatest rate of change?
To compare the slopes:
- Rate of change for bales of hay and mules: \( \frac{1}{2} = 0.5 \)
- Rate of change for cost and square footage of carpet: \( 1.5 \)
Since \( 1.5 \) is greater than \( 0.5 \), we can conclude:
### Response for part c:
**The situation with the greatest rate of change is the cost and square footage of carpet.**
Answered by
GPT-4o mini
To determine the slope for cost and square footage of carpet properly given the options you provided, let’s clarify the calculation again.
### Given Data
- Cost: $30
- Area: 20 square feet
Using a point (20, 30) for this context, let's find the cost per square foot.
### Steps to Calculate the Slope
1. **Slope formula**: As mentioned, the cost per square foot can be derived from:
- Cost per square foot = Total Cost / Total Area
2. **Calculation**:
\[
\text{Slope} = \frac{\text{Total Cost}}{\text{Total Area}} = \frac{30}{20} = \frac{3}{2} = 1.5
\]
### Response Options for Part B
From the options you listed (2, 15, 2, 5, 30, \( \frac{2}{3} \), \( \frac{3}{2} \), 10), the correct slope is clearly:
### Final Choice
**The slope for cost and square footage of carpet is \( \frac{3}{2} \)**.
Given that \( \frac{3}{2} \) is equivalent to 1.5, and it's available in your list, you can select:
**\( \frac{3}{2} \)** as your answer for part B.
### Given Data
- Cost: $30
- Area: 20 square feet
Using a point (20, 30) for this context, let's find the cost per square foot.
### Steps to Calculate the Slope
1. **Slope formula**: As mentioned, the cost per square foot can be derived from:
- Cost per square foot = Total Cost / Total Area
2. **Calculation**:
\[
\text{Slope} = \frac{\text{Total Cost}}{\text{Total Area}} = \frac{30}{20} = \frac{3}{2} = 1.5
\]
### Response Options for Part B
From the options you listed (2, 15, 2, 5, 30, \( \frac{2}{3} \), \( \frac{3}{2} \), 10), the correct slope is clearly:
### Final Choice
**The slope for cost and square footage of carpet is \( \frac{3}{2} \)**.
Given that \( \frac{3}{2} \) is equivalent to 1.5, and it's available in your list, you can select:
**\( \frac{3}{2} \)** as your answer for part B.
Answered by
GPT-4o mini
To derive the equation of a line in slope-intercept form \(y = mx + b\), we need to find the slope \(m\) and the y-intercept \(b\).
### Given Points
- The y-intercept is given as \( (0, 4) \). This means that \( b = 4 \).
- Another point on the line is \( (1, 8) \).
### Step 1: Calculate the Slope (m)
The slope \(m\) can be determined using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 4) \) and \( (1, 8) \):
- \( (x_1, y_1) = (0, 4) \)
- \( (x_2, y_2) = (1, 8) \)
Substituting the values into the slope formula:
\[
m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4
\]
### Step 2: Write the Equation
Now that we have the slope \(m = 4\) and the y-intercept \(b = 4\), we can write the equation of the line in slope-intercept form:
\[
y = mx + b
\]
\[
y = 4x + 4
\]
### Conclusion
The equation of the line in slope-intercept form is:
**\( y = 4x + 4 \)**.
### Given Points
- The y-intercept is given as \( (0, 4) \). This means that \( b = 4 \).
- Another point on the line is \( (1, 8) \).
### Step 1: Calculate the Slope (m)
The slope \(m\) can be determined using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 4) \) and \( (1, 8) \):
- \( (x_1, y_1) = (0, 4) \)
- \( (x_2, y_2) = (1, 8) \)
Substituting the values into the slope formula:
\[
m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4
\]
### Step 2: Write the Equation
Now that we have the slope \(m = 4\) and the y-intercept \(b = 4\), we can write the equation of the line in slope-intercept form:
\[
y = mx + b
\]
\[
y = 4x + 4
\]
### Conclusion
The equation of the line in slope-intercept form is:
**\( y = 4x + 4 \)**.
Answered by
GPT-4o mini
To derive the equation of the line in slope-intercept form ( \( y = mx + b \) ), we need to find the slope ( \( m \) ) and the y-intercept ( \( b \) ).
### Given Points
- The y-intercept is given as \( (0, 2) \). This means that \( b = 2 \).
- Another point on the line is \( (1, -1) \).
### Step 1: Calculate the Slope (m)
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 2) \) and \( (1, -1) \):
- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (1, -1) \)
Substituting these values into the slope formula:
\[
m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3
\]
### Step 2: Write the Equation
Now that we have the slope \( m = -3 \) and the y-intercept \( b = 2 \), we can write the equation of the line in slope-intercept form:
\[
y = mx + b
\]
\[
y = -3x + 2
\]
### Conclusion
The equation of the line in slope-intercept form is:
**\( y = -3x + 2 \)**.
### Given Points
- The y-intercept is given as \( (0, 2) \). This means that \( b = 2 \).
- Another point on the line is \( (1, -1) \).
### Step 1: Calculate the Slope (m)
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 2) \) and \( (1, -1) \):
- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (1, -1) \)
Substituting these values into the slope formula:
\[
m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3
\]
### Step 2: Write the Equation
Now that we have the slope \( m = -3 \) and the y-intercept \( b = 2 \), we can write the equation of the line in slope-intercept form:
\[
y = mx + b
\]
\[
y = -3x + 2
\]
### Conclusion
The equation of the line in slope-intercept form is:
**\( y = -3x + 2 \)**.
Answered by
GPT-4o mini
To derive the equation of the line in slope-intercept form \(y = mx + b\), we need to find the slope \(m\) and the y-intercept \(b\).
### Given Points
- The y-intercept is given as \( (0, -2) \). This means that \( b = -2 \).
- Another point on the line is \( (3, 0) \).
### Step 1: Calculate the Slope (m)
We can use the formula for slope:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, -2) \) and \( (3, 0) \):
- \( (x_1, y_1) = (0, -2) \)
- \( (x_2, y_2) = (3, 0) \)
Substituting the values into the slope formula:
\[
m = \frac{0 - (-2)}{3 - 0} = \frac{0 + 2}{3} = \frac{2}{3}
\]
### Step 2: Write the Equation
Now that we have the slope \(m = \frac{2}{3}\) and the y-intercept \(b = -2\), we can write the equation of the line in slope-intercept form:
\[
y = mx + b
\]
\[
y = \frac{2}{3}x - 2
\]
### Conclusion
The equation of the line in slope-intercept form is:
**\( y = \frac{2}{3}x - 2 \)**.
### Given Points
- The y-intercept is given as \( (0, -2) \). This means that \( b = -2 \).
- Another point on the line is \( (3, 0) \).
### Step 1: Calculate the Slope (m)
We can use the formula for slope:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, -2) \) and \( (3, 0) \):
- \( (x_1, y_1) = (0, -2) \)
- \( (x_2, y_2) = (3, 0) \)
Substituting the values into the slope formula:
\[
m = \frac{0 - (-2)}{3 - 0} = \frac{0 + 2}{3} = \frac{2}{3}
\]
### Step 2: Write the Equation
Now that we have the slope \(m = \frac{2}{3}\) and the y-intercept \(b = -2\), we can write the equation of the line in slope-intercept form:
\[
y = mx + b
\]
\[
y = \frac{2}{3}x - 2
\]
### Conclusion
The equation of the line in slope-intercept form is:
**\( y = \frac{2}{3}x - 2 \)**.
Answered by
GPT-4o mini
In the equation \( y = -2x + 2 \), the slope is the coefficient of \( x \).
### Slope
- From the equation, the coefficient of \( x \) is \(-2\).
### Final Answer
**The slope is -2.**
### Slope
- From the equation, the coefficient of \( x \) is \(-2\).
### Final Answer
**The slope is -2.**
Answered by
GPT-4o mini
In the equation \( y = \frac{3}{4}x - 2 \), the y-intercept is the point where the line intersects the y-axis. This occurs when \( x = 0 \).
### To find the y-intercept:
When \( x = 0 \):
\[
y = \frac{3}{4}(0) - 2 = -2
\]
### Final Answer
**The y-intercept is (0, -2).**
### To find the y-intercept:
When \( x = 0 \):
\[
y = \frac{3}{4}(0) - 2 = -2
\]
### Final Answer
**The y-intercept is (0, -2).**
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