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).

Step2: Plot the y - intercept

The y - intercept is \( (0,-7) \). Locate the point \( (0,-7) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{4}{5} \) means "rise over run", so from the y - intercept \( (0,-7) \), we rise 4 units (upwards) and run 5 units (to the right). So the new point will be \( (0 + 5,-7+4)=(5,-3) \). We can also go in the opposite direction: rise - 4 units (downwards) and run - 5 units (to the left) from \( (0,-7) \) to get \( (0-5,-7 - 4)=(-5,-11) \).

Step4: Draw the line

Connect the points (for example, \( (0,-7) \) and \( (5,-3) \) or other points found using the slope) with a straight line.

(Note: The given graph in the problem is incorrect as it does not represent the line \( y=\frac{4}{5}x - 7 \). The correct graph should pass through \( (0,-7) \) and have a slope of \( \frac{4}{5} \).)

Answer:

To graph \( y=\frac{4}{5}x - 7 \), plot the y - intercept \( (0,-7) \), then use the slope \( \frac{4}{5} \) to find another point (e.g., \( (5,-3) \)) and draw a straight line through these points.