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 y - axis.

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 4 units (upwards) and run 5 units (to the right). So we move from \( (0,-7) \) to \( (0 + 5,-7+4)=(5,-3) \). We can also go in the opposite direction: rise - 4 units (downwards) and run - 5 units (to the left) from \( (0,-7) \) to get \( (0-5,-7 - 4)=(-5,-11) \).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \( (0,-7) \), \( (5,-3) \), \( (-5,-11) \)) to graph the line \( y=\frac{4}{5}x - 7 \).

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 additional points (e.g., from \( (0,-7) \), moving 5 units right and 4 units up gives \( (5,-3) \), moving 5 units left and 4 units down gives \( (-5,-11) \)).
3. Draw a straight line through the plotted points.