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: Find a second point using the slope

The slope \( m = \frac{4}{5} \) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x} \). Starting from the y - intercept \( (0,-7) \), 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). So from \( (0,-7) \), adding 4 to the y - coordinate and 5 to the x - coordinate, we get the point \( (0 + 5,-7+4)=(5,-3) \).

Step3: Plot the points and draw the line

Plot the points \( (0,-7) \) and \( (5,-3) \) on the coordinate plane. Then draw a straight line through these two points. The line should have a positive slope (going up from left to right) since the slope \( \frac{4}{5} \) is positive, and it crosses the y - axis at \( y=-7 \).

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 units and right 5 units to get \( (5,-3) \), then plot \( (5,-3) \).
3. Draw a straight line through \( (0,-7) \) and \( (5,-3) \).