Question

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

Explanation:

Step1: Identify the slope and y-intercept

The equation is in 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 y - axis.

Step3: Use the slope to find another point

The slope \(m=\frac{4}{5}\) means "rise over run", or \(\frac{\text{change in }y}{\text{change in }x}\). So from the point \((0,-7)\), we move up 4 units (because the numerator of the slope is 4) and then move to the right 5 units (because the denominator of the slope is 5). This gives us the point \((0 + 5,-7+4)=(5,-3)\). We can also move down 4 units and left 5 units from \((0,-7)\) to get another point \((0 - 5,-7-4)=(-5,-11)\).

Step4: Draw the line

Draw a straight line through the points \((0,-7)\), \((5,-3)\) (or other points found using the slope) to graph the line \(y=\frac{4}{5}x-7\).

Answer:

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

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