Question

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

Explanation:

Step1: Identify the equation type

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

Step2: Find the y - intercept

The y - intercept is the point where \( x = 0 \). Substitute \( x = 0 \) into the equation: \( y=\frac{4}{5}(0)-7=-7 \). So the y - intercept is \( (0,-7) \).

Step3: Use the slope to find another point

The slope \( m=\frac{4}{5} \) means that for a run of 5 (change in \( x \)), the rise is 4 (change in \( y \)). Starting from the y - intercept \( (0,-7) \), 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 the point \( (5,-3) \) is on the line.

We can also find the x - intercept by setting \( y = 0 \):

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To graph the line, we can plot the y - intercept \( (0,-7) \) and then use the slope to plot other points (like \( (5,-3) \) or \( (8.75,0) \)) and draw a straight line through them. The current graph in the image is incorrect (it's a horizontal line \( y = 5 \)) as it does not represent \( y=\frac{4}{5}x-7 \).

Answer:

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

1. Plot the y - intercept \( (0,-7) \) (where \( x = 0 \), \( y=-7 \)).
2. Use the slope \( \frac{4}{5} \): from \( (0,-7) \), move 5 units right (to \( x = 5 \)) and 4 units up (to \( y=-7 + 4=-3 \)) to plot the point \( (5,-3) \).
3. Draw a straight line through these (and other) points. The given graph (horizontal line \( y = 5 \)) is not the graph of \( y=\frac{4}{5}x-7 \).