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). The y - intercept is the point where \( x = 0 \), so when \( x = 0 \), \( y=-7 \). But the given graph has a horizontal line (slope \( m = 0 \)) which is incorrect for the equation \( y=\frac{4}{5}x-7 \) (slope \( m=\frac{4}{5}
eq0 \)). To graph the correct line:

Step2: Find two points on the line

• Find the y - intercept: When \( x = 0 \), substitute into \( y=\frac{4}{5}x-7 \). Then \( y=\frac{4}{5}(0)-7=-7 \). So one point is \( (0,-7) \).
• Find another point using the slope: The slope \( m=\frac{4}{5}=\frac{\text{rise}}{\text{run}} \). From the point \( (0,-7) \), we rise 4 units (since rise is positive) and run 5 units to the right. So we add 4 to the y - coordinate and 5 to the x - coordinate. \( x=0 + 5=5 \), \( y=-7 + 4=-3 \). So another point is \( (5,-3) \).

We can also find a point by setting \( y = 0 \) and solving for \( x \):
\( 0=\frac{4}{5}x-7 \)

Step3: Solve for x when \( y = 0 \)

Add 7 to both sides: \( 7=\frac{4}{5}x \)
Multiply both sides by \( \frac{5}{4} \): \( x=\frac{35}{4}=8.75 \)
So the x - intercept is \( (8.75,0) \)

To graph the line \( y=\frac{4}{5}x - 7 \), plot the points \( (0,-7) \) and \( (5,-3) \) (or \( (8.75,0) \) and \( (0,-7) \)) and draw a straight line through them. The given graph is incorrect as it represents a horizontal line (slope 0) while the equation has a slope of \( \frac{4}{5} \).

Answer:

The given graph is incorrect. To graph \( y=\frac{4}{5}x - 7 \), plot the y - intercept \( (0,-7) \) and use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0,-7) \), move 5 units right and 4 units up to get \( (5,-3) \)) and draw a line through these points.