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 go up 4 units (rise) and then 5 units to the right (run). So the new point will be \( (0 + 5,-7 + 4)=(5,-3) \).

We can also find the x - intercept by setting \( y = 0 \):
\( 0=\frac{4}{5}x-7 \)
\( \frac{4}{5}x=7 \)
\( x=\frac{35}{4}=8.75 \)

Now, to graph the line \( y=\frac{4}{5}x - 7 \), we plot the y - intercept \( (0,-7) \) and the point \( (5,-3) \) (or the x - intercept \( (8.75,0) \)) and draw a straight line through them. The given graph in the problem is incorrect as it shows a horizontal line \( y = 5 \) instead of the line \( y=\frac{4}{5}x-7 \). To correctly graph \( y=\frac{4}{5}x - 7 \):

1. Plot the y - intercept \( (0,-7) \) (on the y - axis, 7 units below the origin).
2. From \( (0,-7) \), move up 4 units and then 5 units to the right to get the point \( (5,-3) \).
3. Draw a straight line passing through \( (0,-7) \) and \( (5,-3) \).

Answer:

To graph \( y=\frac{4}{5}x - 7 \), plot the y - intercept \( (0,-7) \) and the point \( (5,-3) \) (found using slope \( \frac{4}{5} \)) and draw a line through them. The given graph is incorrect; the correct line has a slope of \( \frac{4}{5} \) and y - intercept at \( (0,-7) \).