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

To find the y - intercept, set \( x = 0 \). Substitute \( x = 0 \) into the equation \( y=\frac{4}{5}(0)-7 \).
\( y=0 - 7=-7 \). So the y - intercept is the point \( (0,-7) \).

Step3: Use the slope to find another point

The slope \( m=\frac{4}{5} \) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x} \). From the y - intercept \( (0,-7) \), we can move up 4 units (since the numerator of the slope is 4) and then move to the right 5 units (since the denominator of the slope is 5).
Moving up 4 from \( y=-7 \) gives \( y=-7 + 4=-3 \), and moving right 5 from \( x = 0 \) gives \( x=0 + 5 = 5 \). So another point on the line is \( (5,-3) \).

Step4: Graph the line

Plot the points \( (0,-7) \) (y - intercept) and \( (5,-3) \) on the coordinate plane and then draw a straight line through them.

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 these points.