Question

graph $y = \frac{4}{5}x - 7$.

Explanation:

Step1: Identify the slope and y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=\frac{4}{5}x - 7\), the slope \(m=\frac{4}{5}\) and the y - intercept \(b=- 7\).

Step2: Plot the y - intercept

The y - intercept is the point where \(x = 0\). Substituting \(x = 0\) into the equation \(y=\frac{4}{5}(0)-7=-7\). So we plot the point \((0,-7)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{4}{5}\) can be thought of as \(\frac{\text{rise}}{\text{run}}\), which means we move up 4 units (since the numerator is positive) and then move to the right 5 units (since the denominator is positive) from the y - intercept point \((0,-7)\).
Starting from \((0,-7)\), moving up 4 units gives \(y=-7 + 4=-3\) and moving right 5 units gives \(x = 0+5 = 5\). So the new point is \((5,-3)\). We can also move down 4 units and left 5 units from the y - intercept. Moving down 4 units from \((0,-7)\) gives \(y=-7-4=-11\) and moving left 5 units gives \(x=0 - 5=-5\), so the point is \((-5,-11)\).

Step4: Draw the line

After plotting two (or more) points on the line (e.g., \((0,-7)\) and \((5,-3)\) or \((0,-7)\) and \((-5,-11)\)), we draw a straight line passing through these points.

(Note: The original graph in the problem seems incorrect as it shows a horizontal line, but the correct graph should be a non - horizontal line with slope \(\frac{4}{5}\) and y - intercept at \((0,-7)\))

Answer:

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

1. Plot the y - intercept \((0,-7)\).
2. Use the slope \(\frac{4}{5}\) (rise = 4, run = 5) to find another point (e.g., from \((0,-7)\), moving up 4 and right 5 gives \((5,-3)\)).
3. Draw a straight line through the plotted points.