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

Step2: Plot the y - intercept

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

Step3: Use the slope to find another point

The slope \( m = \frac{4}{5}\) can be interpreted as "rise over run", that is, for a run (change in x) of 5 units, the rise (change in y) is 4 units. Starting from the y - intercept \((0,-7)\), if we move 5 units to the right (increase x by 5) to \(x = 5\), and then 4 units up (increase y by 4) from \(y=-7\), we get \(y=-7 + 4=-3\). So another point on the line is \((5,-3)\).

Step4: Draw the line

Draw a straight line passing through the points \((0,-7)\) and \((5,-3)\) (and other points found using the slope if needed).

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 5 units right and 4 units up to get \((5,-3)\)).
3. Draw a straight line through these points.