Question

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

Explanation:

Step1: Identify the slope and y-intercept

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). So the line crosses the y - axis at \( (0,-7) \).

Step2: Use the slope to find another point

The slope \( m = \frac{4}{5} \) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x} \). From the y - intercept \( (0,-7) \), we can move up 4 units (since the numerator of the slope is 4) and then move to the right 5 units (since the denominator of the slope is 5). So from \( (0,-7) \), adding 4 to the y - coordinate and 5 to the x - coordinate 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: \( (0-5,-7 - 4)=(-5,-11) \).

Step3: Plot the points and draw the line

First, plot the y - intercept \( (0,-7) \). Then plot the other points we found, like \( (5,-3) \) or \( (-5,-11) \). After that, draw a straight line through these points. The incorrect line in the given graph (the horizontal line at \( y = 5 \)) is wrong. The correct line should have a slope of \( \frac{4}{5} \) and pass through \( (0,-7) \) and other points calculated using the slope.

Answer:

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

1. Plot the y - intercept at \( (0,-7) \).
2. Use the slope \( \frac{4}{5} \) 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 these points. The line in the provided graph (horizontal at \( y = 5 \)) is incorrect; the correct line has a positive slope and passes through \( (0,-7) \) and \( (5,-3) \) (or similar points from the slope calculation).