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 a second point using the slope

The slope \( m=\frac{4}{5}=\frac{\text{rise}}{\text{run}} \). From the y - intercept \( (0,-7) \), we can move up 4 units (rise) and then 5 units to the right (run) to get the next point. So starting from \( (0,-7) \), adding 4 to the y - coordinate and 5 to the x - coordinate, we get the point \( (0 + 5,-7+4)=(5,-3) \).

Step3: Plot the points and draw the line

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

Answer:

To graph \( y=\frac{4}{5}x - 7 \), plot the y - intercept \( (0,-7) \) and the point \( (5,-3) \) (found using the slope \( \frac{4}{5} \)) and draw a line through them.