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 y - axis.

Step3: Use the slope to find another point

The slope \( m=\frac{4}{5}=\frac{\text{rise}}{\text{run}} \). From the point \( (0, - 7) \), we 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). This gives us the point \( (0 + 5,-7 + 4)=(5,-3) \).

Step4: Draw the line

Draw a straight line through the points \( (0,-7) \) and \( (5,-3) \).

(Note: The current graph in the image is incorrect as it shows a horizontal line, but the correct graph should be a line with slope \( \frac{4}{5} \) passing through \( (0,-7) \) and \( (5,-3) \))

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