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 \( m=\frac{4}{5} \) (the slope) and \( b=- 7 \) (the 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 \( m = \frac{4}{5}\) means "rise over run", or \( \frac{\text{change in }y}{\text{change in }x}\). From the point \( (0,-7) \), we move up 4 units (because the numerator of the slope is 4, positive means up) and then move to the right 5 units (because the denominator of the slope is 5, positive means right). This gives us the point \( (0 + 5,-7+4)=(5,-3) \). We can also move down 4 units and left 5 units from \( (0,-7) \) to get another point \( (0 - 5,-7-4)=(-5,-11) \).

Step4: Draw the line

Draw a straight line through the points that we have plotted (such as \( (0,-7) \) and \( (5,-3) \) or \( (0,-7) \) and \( (-5,-11) \)) to graph the equation \( y=\frac{4}{5}x - 7 \).

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