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: Plot the y - intercept

The y - intercept is \( b=-7 \), so we plot 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", that is, 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: Draw the line

Draw a straight line passing through the points \( (0,-7) \) and \( (5,-3) \). This line represents the graph of the equation \( y=\frac{4}{5}x - 7 \).

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: from \( (0,-7) \), move 5 units right and 4 units up to get \( (5,-3) \).
3. Draw a line through \( (0,-7) \) and \( (5,-3) \).