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

Step3: Use the slope to find another point

The slope \( m=\frac{4}{5}=\frac{\text{rise}}{\text{run}} \). From the y - intercept \( (0,-7) \), we can rise 4 units (since the numerator of the slope is 4) and run 5 units to the right (since the denominator of the slope is 5). So the new point is \( (0 + 5,-7+4)=(5,-3) \). We can also go in the opposite direction: rise - 4 units (or fall 4 units) and run - 5 units (or move 5 units to the left). From \( (0,-7) \), moving 5 units left and 4 units down gives \( (0 - 5,-7-4)=(-5,-11) \).

Step4: Plot the points and draw the line

Plot the points \( (0,-7) \), \( (5,-3) \), and \( (-5,-11) \) on the coordinate plane and then draw a straight line through them.

Answer:

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

1. Plot the y - intercept \( (0,-7) \).
2. Use the slope \( \frac{4}{5} \) to find additional points (e.g., \( (5,-3) \) by moving 5 right and 4 up from \( (0,-7) \), or \( (-5,-11) \) by moving 5 left and 4 down from \( (0,-7) \)).
3. Draw a straight line through the plotted points.