Question

graph $y = \frac{4}{5}x - 7$. graph with x-axis from -9 to 9 and y-axis from -9 to 9, grid lines, and a horizontal blue line with two green dots at (-5,5) and (6,5)

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 \(x = 0\). When \(x = 0\), \(y=-7\). So we plot the point \((0,-7)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{4}{5}\) means that 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 \(5\)) and \(4\) units up (increase \(y\) by \(4\)), we get the point \((0 + 5,-7+4)=(5,-3)\). We can also move in the opposite direction: from \((0,-7)\), move \(5\) units to the left (decrease \(x\) by \(5\)) and \(4\) units down (decrease \(y\) by \(4\)) to get the point \((0 - 5,-7-4)=(-5,-11)\).

Step4: Draw the line

After plotting two or more points (e.g., \((0,-7)\) and \((5,-3)\) or \((0,-7)\) and \((-5,-11)\)), we draw a straight line passing through these points. The original graph in the problem is incorrect as it shows a horizontal line, but the correct graph should be a line with a slope of \(\frac{4}{5}\) 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 \(\frac{4}{5}\) 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 the plotted points. The correct graph is a non - horizontal line with slope \(\frac{4}{5}\) and y - intercept at \((0,-7)\).