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 \( m \) is the slope and \( b \) is the y-intercept. Here, \( m=\frac{4}{5} \) and \( b = -7 \).

Step2: Plot the y-intercept

The y-intercept \( b = -7 \) means the line crosses the y-axis at \( (0, -7) \). Locate the point \( (0, -7) \) on the graph.

Step3: Use the slope to find another point

The slope \( m=\frac{4}{5} \) means "rise over run", so from the y-intercept \( (0, -7) \), we move up 4 units (rise) and right 5 units (run). This gives the point \( (0 + 5, -7 + 4) = (5, -3) \). Alternatively, we can move down 4 units and left 5 units from the y-intercept to get \( (0 - 5, -7 - 4) = (-5, -11) \), but \( (5, -3) \) is easier to plot on the given grid.

Step4: Draw the line

Connect the points \( (0, -7) \) and \( (5, -3) \) (or other points found using the slope) with a straight line. The existing line in the image is incorrect; the correct line should pass through \( (0, -7) \) and have a slope of \( \frac{4}{5} \).

Answer:

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

1. Plot the y - intercept at \( (0, -7) \).
2. Use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0, -7) \), move up 4, right 5 to get \( (5, -3) \)).
3. Draw a straight line through these points. The correct graph should have a line passing through \( (0, -7) \) and \( (5, -3) \) (or similar points from the slope), not the horizontal line shown.