Question

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

Explanation:

Step1: Identify the slope-intercept form

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).

Step2: Find the y - intercept

The y - intercept \( b=-7 \), so the line crosses the y - axis at the point \( (0,-7) \).

Step3: Use the slope to find another point

The slope \( m = \frac{4}{5}\) means for a run (change in \( x \)) of 5 units, the rise (change in \( y \)) is 4 units. Starting from the y - intercept \( (0,-7) \), if we move 5 units to the right (increase \( x \) by 5, so \( x = 0+5 = 5 \)) and 4 units up (increase \( y \) by 4, so \( y=-7 + 4=-3 \)), we get the point \( (5,-3) \).

Step4: Graph the line

Plot the points \( (0,-7) \) and \( (5,-3) \) (and other points if needed) and draw a straight line through them. The given graph in the problem is incorrect as it shows a horizontal line (which would have a slope of 0, but our line has a slope of \( \frac{4}{5}\)). To correctly graph \( y=\frac{4}{5}x - 7 \), we use the two points we found.

Answer:

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

1. Plot the y - intercept at \( (0,-7) \) (since when \( x = 0 \), \( y=-7 \)).
2. Use the slope \( \frac{4}{5} \): from \( (0,-7) \), move 5 units right (to \( x = 5 \)) and 4 units up (to \( y=-7 + 4=-3 \)) to get the point \( (5,-3) \).
3. Draw a straight line through \( (0,-7) \) and \( (5,-3) \). The original graph in the problem is incorrect (it's a horizontal line, but this line has a non - zero slope).