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).

Step2: Plot the y - intercept

The y - intercept is \( b=-7 \), so we plot the point \( (0,-7) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{4}{5}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,-7) \), we rise (move up) 4 units and run (move right) 5 units. So we get the point \( (0 + 5,-7+4)=(5,-3) \). We can also go in the opposite direction: from \( (0,-7) \), rise - 4 (move down 4 units) and run - 5 (move left 5 units) to get the point \( (0 - 5,-7-4)=(-5,-11) \).

Step4: Draw the line

Draw a straight line through the points we found (e.g., \( (0,-7) \) and \( (5,-3) \)) to graph the equation \( y=\frac{4}{5}x - 7 \).

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 up 4 and right 5 to get \( (5,-3) \)).
3. Draw a line through these points. The line should pass through \( (0,-7) \) and \( (5,-3) \) (and other points found using the slope) and have a positive slope of \( \frac{4}{5} \).