Question
The lines on the graph read through (o,5) (3,3) and (6,1) please answer the following
What is the y-intercept
Wha is the slope
What is the equation of the line in slope-intercept form
This is a proportional or non proportional relationship
What is the y-intercept
Wha is the slope
What is the equation of the line in slope-intercept form
This is a proportional or non proportional relationship
Answers
Answer
For the Y intercept please say if it is one of these answers:
A: (0,0)
B: -5/3
C: y = 5x - 2
D: 7
E: (-5,0)
F: (0,5)
G: 0
H: y = 5x + 2/3
A: (0,0)
B: -5/3
C: y = 5x - 2
D: 7
E: (-5,0)
F: (0,5)
G: 0
H: y = 5x + 2/3
Answer
Ok thanks!
Answer
which equation represents the graph described:
Dot 1: (0,3)
Dot 2: (2, -1)
Answers:
y=−4/5x+3
y is equal to negative 4 fifths x plus 3
y=3x+5
y is equal to 3 x plus 5
y=1/2x−1
y is equal to 1 half x minus 1
y=5/4x+3
Dot 1: (0,3)
Dot 2: (2, -1)
Answers:
y=−4/5x+3
y is equal to negative 4 fifths x plus 3
y=3x+5
y is equal to 3 x plus 5
y=1/2x−1
y is equal to 1 half x minus 1
y=5/4x+3
Answer
Sorry I messed up on dot 2 its actually (1,-1)
Answer
Could you try rearranging the problem such as (3,0) and (-1,1)
Answered by
GPT-4o mini
To analyze the relationship represented by the points (0, 5), (3, 3), and (6, 1), we can determine the y-intercept, slope, equation of the line in slope-intercept form, and whether it is proportional or non-proportional.
### 1. Y-intercept
The y-intercept is the value of \( y \) at \( x = 0 \). From the points provided, when \( x = 0 \), the value of \( y \) is \( 5 \).
**Y-intercept: 5**
### 2. Slope
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can choose any two points, but let's use (0, 5) and (3, 3):
\[
m = \frac{3 - 5}{3 - 0} = \frac{-2}{3} = -\frac{2}{3}
\]
**Slope: -\(\frac{2}{3}\)**
### 3. Equation of the line in slope-intercept form
The slope-intercept form of the equation of a line is given by:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept. Substituting the values we found:
\[
y = -\frac{2}{3}x + 5
\]
**Equation of the line: \( y = -\frac{2}{3}x + 5 \)**
### 4. Proportional or Non-Proportional Relationship
A proportional relationship means that the line passes through the origin (0,0). Since the y-intercept here is 5 (not 0), this indicates that the relationship is **non-proportional**.
**Conclusion:**
- Y-intercept: \( 5 \)
- Slope: \( -\frac{2}{3} \)
- Equation of the line: \( y = -\frac{2}{3}x + 5 \)
- The relationship is non-proportional.
### 1. Y-intercept
The y-intercept is the value of \( y \) at \( x = 0 \). From the points provided, when \( x = 0 \), the value of \( y \) is \( 5 \).
**Y-intercept: 5**
### 2. Slope
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can choose any two points, but let's use (0, 5) and (3, 3):
\[
m = \frac{3 - 5}{3 - 0} = \frac{-2}{3} = -\frac{2}{3}
\]
**Slope: -\(\frac{2}{3}\)**
### 3. Equation of the line in slope-intercept form
The slope-intercept form of the equation of a line is given by:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept. Substituting the values we found:
\[
y = -\frac{2}{3}x + 5
\]
**Equation of the line: \( y = -\frac{2}{3}x + 5 \)**
### 4. Proportional or Non-Proportional Relationship
A proportional relationship means that the line passes through the origin (0,0). Since the y-intercept here is 5 (not 0), this indicates that the relationship is **non-proportional**.
**Conclusion:**
- Y-intercept: \( 5 \)
- Slope: \( -\frac{2}{3} \)
- Equation of the line: \( y = -\frac{2}{3}x + 5 \)
- The relationship is non-proportional.
Answered by
GPT-4o mini
The y-intercept of the line, which is the point where the line crosses the y-axis, is (0, 5) based on the information provided.
From the options you've listed, the correct answer is:
**F: (0, 5)**
From the options you've listed, the correct answer is:
**F: (0, 5)**
Answered by
GPT-4o mini
You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy learning!
Answered by
GPT-4o mini
To determine which equation represents the graph defined by the points (0, 3) and (2, -1), we first need to find the slope and then use the slope-intercept form to identify the correct equation.
### 1. Finding the slope
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 3) \) and \( (2, -1) \):
- \( (x_1, y_1) = (0, 3) \)
- \( (x_2, y_2) = (2, -1) \)
Substituting these values into the slope formula:
\[
m = \frac{-1 - 3}{2 - 0} = \frac{-4}{2} = -2
\]
### 2. Using the slope to write the equation
Now that we have the slope \( m = -2 \) and we know the y-intercept is \( 3 \) (from the point (0, 3)), we can write the equation in slope-intercept form \( y = mx + b \):
\[
y = -2x + 3
\]
### 3. Checking the answer choices
Let's now check the given answer choices:
1. **y = -4/5x + 3** (slope is -4/5)
2. **y = 3x + 5** (slope is 3)
3. **y = 1/2x - 1** (slope is 1/2)
4. **y = 5/4x + 3** (slope is 5/4)
None of the provided equations match the equation we derived \( y = -2x + 3 \).
Therefore, based on the calculations, none of the given options correctly represent the equation for the line passing through the points (0, 3) and (2, -1). If the answer choices were intended to include this line, please double-check the options or the points provided.
### 1. Finding the slope
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 3) \) and \( (2, -1) \):
- \( (x_1, y_1) = (0, 3) \)
- \( (x_2, y_2) = (2, -1) \)
Substituting these values into the slope formula:
\[
m = \frac{-1 - 3}{2 - 0} = \frac{-4}{2} = -2
\]
### 2. Using the slope to write the equation
Now that we have the slope \( m = -2 \) and we know the y-intercept is \( 3 \) (from the point (0, 3)), we can write the equation in slope-intercept form \( y = mx + b \):
\[
y = -2x + 3
\]
### 3. Checking the answer choices
Let's now check the given answer choices:
1. **y = -4/5x + 3** (slope is -4/5)
2. **y = 3x + 5** (slope is 3)
3. **y = 1/2x - 1** (slope is 1/2)
4. **y = 5/4x + 3** (slope is 5/4)
None of the provided equations match the equation we derived \( y = -2x + 3 \).
Therefore, based on the calculations, none of the given options correctly represent the equation for the line passing through the points (0, 3) and (2, -1). If the answer choices were intended to include this line, please double-check the options or the points provided.
Answered by
GPT-4o mini
No problem! Let's recalculate the slope and the equation using the correct points: (0, 3) and (1, -1).
### 1. Finding the slope
Using the points \( (0, 3) \) and \( (1, -1) \):
- \( (x_1, y_1) = (0, 3) \)
- \( (x_2, y_2) = (1, -1) \)
Now, we can calculate the slope \( m \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 3}{1 - 0} = \frac{-4}{1} = -4
\]
### 2. Using the slope to write the equation
Now that we have the slope \( m = -4 \) and we know that the y-intercept is \( 3 \) (from the point (0, 3)), we can write the equation in slope-intercept form \( y = mx + b \):
\[
y = -4x + 3
\]
### 3. Checking the answer choices
Now let's check the provided answer choices against the equation we derived:
1. **y = -4/5x + 3** (slope is -4/5)
2. **y = 3x + 5** (slope is 3)
3. **y = 1/2x - 1** (slope is 1/2)
4. **y = 5/4x + 3** (slope is 5/4)
None of the given options match \( y = -4x + 3 \).
### Conclusion
Again, it appears that none of the provided equations accurately represent the line defined by the points (0, 3) and (1, -1). Please feel free to provide more information or check for any possible error in the response options!
### 1. Finding the slope
Using the points \( (0, 3) \) and \( (1, -1) \):
- \( (x_1, y_1) = (0, 3) \)
- \( (x_2, y_2) = (1, -1) \)
Now, we can calculate the slope \( m \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 3}{1 - 0} = \frac{-4}{1} = -4
\]
### 2. Using the slope to write the equation
Now that we have the slope \( m = -4 \) and we know that the y-intercept is \( 3 \) (from the point (0, 3)), we can write the equation in slope-intercept form \( y = mx + b \):
\[
y = -4x + 3
\]
### 3. Checking the answer choices
Now let's check the provided answer choices against the equation we derived:
1. **y = -4/5x + 3** (slope is -4/5)
2. **y = 3x + 5** (slope is 3)
3. **y = 1/2x - 1** (slope is 1/2)
4. **y = 5/4x + 3** (slope is 5/4)
None of the given options match \( y = -4x + 3 \).
### Conclusion
Again, it appears that none of the provided equations accurately represent the line defined by the points (0, 3) and (1, -1). Please feel free to provide more information or check for any possible error in the response options!
Answered by
GPT-4o mini
Sure! Let's find the equation of the line defined by the points (3, 0) and (-1, 1).
### 1. Finding the slope
Using the points \( (3, 0) \) and \( (-1, 1) \):
- \( (x_1, y_1) = (3, 0) \)
- \( (x_2, y_2) = (-1, 1) \)
The slope \( m \) is calculated as follows:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{-1 - 3} = \frac{1}{-4} = -\frac{1}{4}
\]
### 2. Using the slope to write the equation
Using the slope \( m = -\frac{1}{4} \) and the y-intercept, we can find the y-intercept by substituting one of the points into the slope-intercept form of the equation \( y = mx + b \).
Let's use the point \( (3, 0) \):
\[
0 = -\frac{1}{4}(3) + b
\]
\[
0 = -\frac{3}{4} + b
\]
\[
b = \frac{3}{4}
\]
So the y-intercept is \( \frac{3}{4} \).
Putting this all together, the equation in slope-intercept form is:
\[
y = -\frac{1}{4}x + \frac{3}{4}
\]
### 3. Checking with the answer choices
Now let's check this derived equation against the provided answer choices:
1. **y = -4/5x + 3** (slope is -4/5)
2. **y = 3x + 5** (slope is 3)
3. **y = 1/2x - 1** (slope is 1/2)
4. **y = 5/4x + 3** (slope is 5/4)
None of the given options match \( y = -\frac{1}{4}x + \frac{3}{4} \).
### Conclusion
The equation representing the line going through the points (3, 0) and (-1, 1) is:
\[
y = -\frac{1}{4}x + \frac{3}{4}
\]
However, it appears none of the provided options represent this equation. If you have other points or options, please share them!
### 1. Finding the slope
Using the points \( (3, 0) \) and \( (-1, 1) \):
- \( (x_1, y_1) = (3, 0) \)
- \( (x_2, y_2) = (-1, 1) \)
The slope \( m \) is calculated as follows:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{-1 - 3} = \frac{1}{-4} = -\frac{1}{4}
\]
### 2. Using the slope to write the equation
Using the slope \( m = -\frac{1}{4} \) and the y-intercept, we can find the y-intercept by substituting one of the points into the slope-intercept form of the equation \( y = mx + b \).
Let's use the point \( (3, 0) \):
\[
0 = -\frac{1}{4}(3) + b
\]
\[
0 = -\frac{3}{4} + b
\]
\[
b = \frac{3}{4}
\]
So the y-intercept is \( \frac{3}{4} \).
Putting this all together, the equation in slope-intercept form is:
\[
y = -\frac{1}{4}x + \frac{3}{4}
\]
### 3. Checking with the answer choices
Now let's check this derived equation against the provided answer choices:
1. **y = -4/5x + 3** (slope is -4/5)
2. **y = 3x + 5** (slope is 3)
3. **y = 1/2x - 1** (slope is 1/2)
4. **y = 5/4x + 3** (slope is 5/4)
None of the given options match \( y = -\frac{1}{4}x + \frac{3}{4} \).
### Conclusion
The equation representing the line going through the points (3, 0) and (-1, 1) is:
\[
y = -\frac{1}{4}x + \frac{3}{4}
\]
However, it appears none of the provided options represent this equation. If you have other points or options, please share them!