Question

graph $y = \frac{4}{5}x - 7$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = \frac{4}{5}x - 7 \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{4}{5} \) (slope) and \( b=-7 \) (y - intercept). So the line crosses the y - axis at the point \( (0,-7) \).

Step2: Find another point using the slope

The slope \( m = \frac{4}{5}\) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x}=\frac{4}{5} \). Starting from the y - intercept \( (0,-7) \), we can move up 4 units (change in y) and then move 5 units to the right (change in x). So from \( (0,-7) \), moving up 4 gives \( y=-7 + 4=-3 \) and moving right 5 gives \( x = 0+5 = 5 \). So we get the point \( (5,-3) \).

Step3: Plot the points and draw the line

First, plot the y - intercept \( (0,-7) \) on the coordinate plane. Then plot the point \( (5,-3) \) that we found using the slope. Finally, draw a straight line through these two points.

(Note: The original graph in the problem is incorrect as it shows a horizontal line \( y = 5 \) instead of the line for \( y=\frac{4}{5}x-7 \). The correct graph should pass through \( (0, - 7) \) and \( (5,-3) \) (and other points found using the slope) with a positive slope of \( \frac{4}{5} \))

Answer:

To graph \( y=\frac{4}{5}x - 7 \):

1. Plot the y - intercept at \( (0,-7) \).
2. Use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0,-7) \), move up 4 and right 5 to get \( (5,-3) \)).
3. Draw a straight line through the plotted points. The original graph provided is incorrect; the correct line has a slope of \( \frac{4}{5} \) and a y - intercept of \( - 7 \).