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 for every increase of 5 units in the \(x\) - direction (run), the \(y\) - value increases by 4 units (rise). Starting from the point \((0,-7)\), if we move 5 units to the right (increase \(x\) by 5) to \(x = 5\) and 4 units up (increase \(y\) by 4) from \(y=-7\), we get \(y=-7 + 4=-3\). So we plot the point \((5,-3)\).

Step4: Draw the line

Using a straightedge, draw a line that passes through the points \((0,-7)\) and \((5,-3)\). We can also find more points by using the slope in the opposite direction (for example, move 5 units to the left (decrease \(x\) by 5) and 4 units down (decrease \(y\) by 4) from \((0,-7)\) to get \((- 5,-11)\)) and draw the line through these points as well.

Answer:

To graph \(y = \frac{4}{5}x-7\), plot the y - intercept \((0, - 7)\) and then use the slope \(\frac{4}{5}\) (rise 4, run 5) to find another point (e.g., \((5,-3)\)) and draw a straight line through these points. The line should pass through \((0,-7)\) and other points obtained by using the slope, such as \((5,-3)\), \((-5,-11)\) etc.