Question

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

Explanation:

Step1: Identify the slope-intercept form

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 move up 4 units (because the numerator of the slope is 4, rise is positive) and then move 5 units to the right (because the denominator of the slope is 5, run is positive). So, from \( (0,-7) \), moving up 4 and right 5 gives us the point \( (0 + 5,-7 + 4)=(5,-3) \).

Step4: Draw the line

Draw a straight line passing through the points \( (0,-7) \) and \( (5,-3) \). (We can also find more points by using the slope in the opposite direction: from \( (0,-7) \), move down 4 units and left 5 units to get \( (0-5,-7 - 4)=(-5,-11) \) and plot that point too, then draw the line through the three points for better accuracy.)

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 (e.g., \( (5,-3) \) by moving up 4 and right 5 from \( (0,-7) \)).
3. Draw a straight line through the plotted points.