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 y - axis.

Step3: Use the slope to find another point

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

Step4: Draw the line

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

Answer:

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

1. Plot the y - intercept \((0,-7)\) on the y - axis.
2. Use the slope \(\frac{4}{5}\) (rise = 4, run = 5) to find another point. From \((0,-7)\), move up 4 and right 5 to get \((5,-3)\) (or down 4 and left 5 to get \((-5,-11)\)).
3. Draw a straight line through the plotted points.