Question

1. the second linear function has a slope of -4 and an x-intercept at 8. which statement is accurate about the two equations?

x	y
-2	-4
0	-3
4	-1
5	-0.5

a. the slope of the first linear function is positive, while the slope of the second linear function is negative.
b. the x-intercept of the first linear function is greater than the x-intercept of the second linear function.
c. the y-intercept in the second linear function is greater than the y-intercept in the first linear function.
d. the y-intercept in the second linear function is smaller than the y-intercept in the first linear function.

Explanation:

Step1: Find slope of first function

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(x_1,y_1)=(0,-3)$ and $(x_2,y_2)=(4,-1)$:
$m=\frac{-1-(-3)}{4-0}=\frac{2}{4}=0.5$

Step2: Find y-intercept of first function

From table, when $x=0$, $y=-3$. So y-intercept is $-3$.

Step3: Find x-intercept of first function

First, write first function equation: $y=0.5x-3$. Set $y=0$:
$0=0.5x-3 \implies 0.5x=3 \implies x=6$

Step4: Analyze second linear function

Given slope $m=-4$, x-intercept at $x=1$ (since x-intercept is where $y=0$). Write its equation: $y=-4(x-1)=-4x+4$. So y-intercept is $4$.

Step5: Evaluate each option

• Option a: First slope $0.5>0$, second slope $-4<0$. This is true.
• Option b: First x-intercept $6$, second x-intercept $1$. $6>1$, so this is false.
• Option c: Second y-intercept $4$, first y-intercept $-3$. $4>-3$, so this is false.
• Option d: Second y-intercept $4$, first y-intercept $-3$. $4>-3$, so this is false.

Answer:

a. The slope of the first linear function is positive, while the slope of the second linear function is negative.