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). So we move from \( (0,-7) \) to \( (0 + 5,-7+4)=(5,-3) \).

Step4: Draw the line

Now we draw a straight line through the points \( (0,-7) \) and \( (5,-3) \) (and extend it in both directions). The given graph in the problem is incorrect as it shows a horizontal line at \( y = 5 \) instead of the line for \( y=\frac{4}{5}x-7 \). To correctly graph \( y=\frac{4}{5}x - 7 \), we should have a line with a positive slope passing through \( (0,-7) \) and \( (5,-3) \) (and other points obtained by using the slope).

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 (e.g., from \( (0,-7) \), move 4 up and 5 right to get \( (5,-3) \)).
3. Draw a line through these points. The given graph is incorrect; the correct line has a positive slope, passes through \( (0, - 7) \) and \( (5,-3) \) (and extends).