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:
- Start with the y-intercept (0, 5) on the graph.
- 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).
- Plot the second point (3, 3).
- 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.