Question

function 1 and function 2 are both linear functions. the equation for function 1 is $y = \frac{-4}{3}x + 2$. the points $(0, -8)$, $(4, -5)$, and $(8, -2)$ lie on function 2. which statement is correct?
a. the slope of the line for function 1 is greater than the slope of the line for function 2.
b. the slopes of the lines for the functions are negative reciprocals and the lines are perpendicular.
c. the slopes of the lines for the functions are equal and the lines are perpendicular.
d. the slopes of the lines for the functions are equal and the lines are parallel.

Explanation:

Step1: Identify slope of Function 1

Function 1 is in slope-intercept form $y=mx+b$, so slope $m_1 = \frac{-4}{3}$.

Step2: Calculate slope of Function 2

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with points $(0,-8)$ and $(4,-5)$:
$m_2 = \frac{-5 - (-8)}{4 - 0} = \frac{3}{4}$

Step3: Analyze slope relationship

Check if slopes are negative reciprocals: $m_1 \times m_2 = \frac{-4}{3} \times \frac{3}{4} = -1$. Lines with slopes whose product is -1 are perpendicular.

Step4: Evaluate all options

• A: $\frac{-4}{3} < \frac{3}{4}$, so false.
• B: Slopes are negative reciprocals, lines are perpendicular, so true.
• C: Slopes are not equal, so false.
• D: Slopes are not equal, so lines not parallel, false.

Answer:

B. The slopes of the lines for the functions are negative reciprocals and the lines are perpendicular.