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Identify the slope and y intercept. Then, graph the linear equation. y−5=−3xAsked by need help 100%
Identify the slope and y intercept. Then, graph the linear equation.
`y=-\frac{2}{3}x+5`
M?
`y=-\frac{2}{3}x+5`
M?
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GPT-4o mini
To identify the slope and y-intercept from the equation of the line given in slope-intercept form \(y = mx + b\), we need to recognize that:
- \(m\) is the slope
- \(b\) is the y-intercept
From the equation \(y = -\frac{2}{3}x + 5\):
- The slope \(m\) is \(-\frac{2}{3}\).
- The y-intercept \(b\) is \(5\) (which means the line crosses the y-axis at the point \((0, 5)\)).
### Summary:
- Slope (M): \(-\frac{2}{3}\)
- Y-intercept: \(5\)
### Graphing the Equation:
1. Start with the y-intercept (0, 5) on the graph.
2. Use the slope \(-\frac{2}{3}\):
- This means for every 3 units you move to the right (positive x direction), you move 2 units down (negative y direction).
- From (0, 5), if you move 3 units to the right, you go to (3, 5), and then move down 2 units to point (3, 3).
3. Plot the second point (3, 3).
4. Draw a line through the points (0, 5) and (3, 3).
### Graph:
Here’s a description of how the graph would look visually:
- The line goes downward from left to right since the slope is negative.
- It crosses the y-axis at (0, 5).
- The points can be connected with a straight line extending in both directions.
You can use graph paper or plotting software to create the visual representation.
- \(m\) is the slope
- \(b\) is the y-intercept
From the equation \(y = -\frac{2}{3}x + 5\):
- The slope \(m\) is \(-\frac{2}{3}\).
- The y-intercept \(b\) is \(5\) (which means the line crosses the y-axis at the point \((0, 5)\)).
### Summary:
- Slope (M): \(-\frac{2}{3}\)
- Y-intercept: \(5\)
### Graphing the Equation:
1. Start with the y-intercept (0, 5) on the graph.
2. Use the slope \(-\frac{2}{3}\):
- This means for every 3 units you move to the right (positive x direction), you move 2 units down (negative y direction).
- From (0, 5), if you move 3 units to the right, you go to (3, 5), and then move down 2 units to point (3, 3).
3. Plot the second point (3, 3).
4. Draw a line through the points (0, 5) and (3, 3).
### Graph:
Here’s a description of how the graph would look visually:
- The line goes downward from left to right since the slope is negative.
- It crosses the y-axis at (0, 5).
- The points can be connected with a straight line extending in both directions.
You can use graph paper or plotting software to create the visual representation.
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