Question
Identify the slope (`m`) and y-intercept (`b`) by typing them in the boxes below. Then, graph the linear equation.
`y=-\frac{1}{4}x+2`
`y=-\frac{1}{4}x+2`
Answers
GPT-4o mini
In the linear equation \( y = -\frac{1}{4}x + 2 \), the slope (\( m \)) and y-intercept (\( b \)) can be identified as follows:
- **Slope \( m \)**: \(-\frac{1}{4}\)
- **Y-intercept \( b \)**: \(2\)
To graph the equation \( y = -\frac{1}{4}x + 2 \):
1. Start by plotting the y-intercept. The y-intercept is the point where the line crosses the y-axis, which in this case is at the point \((0, 2)\).
2. Use the slope to find another point. The slope of \(-\frac{1}{4}\) means that for every 4 units you move to the right (positive direction along the x-axis), the line moves down 1 unit (negative direction along the y-axis). From the point \((0, 2)\), move 4 units to the right to \((4, 2)\) and then 1 unit down to \((4, 1)\).
3. Plot the point \((4, 1)\) on the graph.
4. Draw a straight line through the points \((0, 2)\) and \((4, 1)\).
This will give you a graph of the linear equation \( y = -\frac{1}{4}x + 2 \).
### Summary
- Slope \( m = -\frac{1}{4} \)
- Y-intercept \( b = 2 \)
You can sketch the line based on these points.
- **Slope \( m \)**: \(-\frac{1}{4}\)
- **Y-intercept \( b \)**: \(2\)
To graph the equation \( y = -\frac{1}{4}x + 2 \):
1. Start by plotting the y-intercept. The y-intercept is the point where the line crosses the y-axis, which in this case is at the point \((0, 2)\).
2. Use the slope to find another point. The slope of \(-\frac{1}{4}\) means that for every 4 units you move to the right (positive direction along the x-axis), the line moves down 1 unit (negative direction along the y-axis). From the point \((0, 2)\), move 4 units to the right to \((4, 2)\) and then 1 unit down to \((4, 1)\).
3. Plot the point \((4, 1)\) on the graph.
4. Draw a straight line through the points \((0, 2)\) and \((4, 1)\).
This will give you a graph of the linear equation \( y = -\frac{1}{4}x + 2 \).
### Summary
- Slope \( m = -\frac{1}{4} \)
- Y-intercept \( b = 2 \)
You can sketch the line based on these points.