Question
Identify the slope and y intercept. Then, graph the linear equation.
y−6=−2x
Begin with
b,the y-intercept:
Type the number only. Do NOT enter a coordinate.
Submit
Move with
m,the slope:
y−6=−2x
Begin with
b,the y-intercept:
Type the number only. Do NOT enter a coordinate.
Submit
Move with
m,the slope:
Answers
GPT-4o mini
To identify the slope and y-intercept from the equation \( y - 6 = -2x \), you can start by rearranging it into slope-intercept form, which is \( y = mx + b \).
1. **Rearranging the equation:**
\[
y = -2x + 6
\]
From this form, we can identify:
- The slope \( m \) is \( -2 \).
- The y-intercept \( b \) is \( 6 \).
**Final answers:**
- **b (the y-intercept):** 6
- **m (the slope):** -2
Now, let’s summarize the results:
- **y-intercept (b):** 6
- **slope (m):** -2
If you need to graph the equation:
1. Plot the y-intercept \( (0, 6) \) on the coordinate plane.
2. From the y-intercept, use the slope. Since the slope is \( -2 \), you go down 2 units for every 1 unit you move to the right.
This would give you another point, and you can draw a line through the two points to graph the equation.
1. **Rearranging the equation:**
\[
y = -2x + 6
\]
From this form, we can identify:
- The slope \( m \) is \( -2 \).
- The y-intercept \( b \) is \( 6 \).
**Final answers:**
- **b (the y-intercept):** 6
- **m (the slope):** -2
Now, let’s summarize the results:
- **y-intercept (b):** 6
- **slope (m):** -2
If you need to graph the equation:
1. Plot the y-intercept \( (0, 6) \) on the coordinate plane.
2. From the y-intercept, use the slope. Since the slope is \( -2 \), you go down 2 units for every 1 unit you move to the right.
This would give you another point, and you can draw a line through the two points to graph the equation.
wrong
GPT-4o mini
I apologize for any confusion in my previous response. Let's go through the equation \( y - 6 = -2x \) step by step to correctly find the slope and y-intercept.
Starting with the given equation:
\[
y - 6 = -2x
\]
### Step 1: Solve for \( y \)
Add 6 to both sides:
\[
y = -2x + 6
\]
### Step 2: Identify the slope and y-intercept
Now, in the slope-intercept form \( y = mx + b \):
- **Slope \( m \)**: The coefficient of \( x \) is \( -2 \).
- **Y-intercept \( b \)**: The constant term is \( 6 \).
### Summary of Results
- **b (the y-intercept):** 6
- **m (the slope):** -2
To clarify:
- **Y-intercept (b):** **6** (not a coordinate)
- **Slope (m):** **-2**
If you graph this line, you'll plot the point at \( (0, 6) \) and then use the slope of \( -2 \) to find another point by going down 2 units and right 1 unit.
Please let me know if you need additional help or if there is anything specific you would like to clarify!
Starting with the given equation:
\[
y - 6 = -2x
\]
### Step 1: Solve for \( y \)
Add 6 to both sides:
\[
y = -2x + 6
\]
### Step 2: Identify the slope and y-intercept
Now, in the slope-intercept form \( y = mx + b \):
- **Slope \( m \)**: The coefficient of \( x \) is \( -2 \).
- **Y-intercept \( b \)**: The constant term is \( 6 \).
### Summary of Results
- **b (the y-intercept):** 6
- **m (the slope):** -2
To clarify:
- **Y-intercept (b):** **6** (not a coordinate)
- **Slope (m):** **-2**
If you graph this line, you'll plot the point at \( (0, 6) \) and then use the slope of \( -2 \) to find another point by going down 2 units and right 1 unit.
Please let me know if you need additional help or if there is anything specific you would like to clarify!
what are the two points?
GPT-4o mini
To find two points on the line represented by the equation \( y = -2x + 6 \), we can choose some values for \( x \) and calculate the corresponding \( y \) values.
### Point 1: Using the y-intercept
The y-intercept occurs when \( x = 0 \):
\[
y = -2(0) + 6 = 6
\]
So, the first point is:
\[
(0, 6)
\]
### Point 2: Choosing another value for \( x \)
Let’s choose \( x = 1 \):
\[
y = -2(1) + 6 = -2 + 6 = 4
\]
So, the second point is:
\[
(1, 4)
\]
### Summary of Points
1. **Point 1 (y-intercept):** \( (0, 6) \)
2. **Point 2 (when \( x = 1 \)):** \( (1, 4) \)
You can also choose other values for \( x \) to find additional points, such as \( x = 2 \):
\[
y = -2(2) + 6 = -4 + 6 = 2
\]
This would give you a third point of \( (2, 2) \).
So with these examples:
- Points \( (0, 6) \), \( (1, 4) \), and \( (2, 2) \) are all valid points on the line defined by the equation \( y = -2x + 6 \).
### Point 1: Using the y-intercept
The y-intercept occurs when \( x = 0 \):
\[
y = -2(0) + 6 = 6
\]
So, the first point is:
\[
(0, 6)
\]
### Point 2: Choosing another value for \( x \)
Let’s choose \( x = 1 \):
\[
y = -2(1) + 6 = -2 + 6 = 4
\]
So, the second point is:
\[
(1, 4)
\]
### Summary of Points
1. **Point 1 (y-intercept):** \( (0, 6) \)
2. **Point 2 (when \( x = 1 \)):** \( (1, 4) \)
You can also choose other values for \( x \) to find additional points, such as \( x = 2 \):
\[
y = -2(2) + 6 = -4 + 6 = 2
\]
This would give you a third point of \( (2, 2) \).
So with these examples:
- Points \( (0, 6) \), \( (1, 4) \), and \( (2, 2) \) are all valid points on the line defined by the equation \( y = -2x + 6 \).