Question

which of the following equations has a graph with a y-intercept of -8?
a. $y = 3x - 8$

b. $y = -8x + 3$

c. $3x - 8y = -5$

d. $-8x + 3y = -5$

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a linear equation is $y = mx + b$, where $b$ is the y-intercept. For equations not in this form, set $x=0$ and solve for $y$ to find the y-intercept.

Step2: Check Option A

Equation: $y = 3x - 8$. This matches $y=mx+b$, so $b=-8$.

Step3: Check Option B

Equation: $y = -8x + 3$. Here, $b=3$, not $-8$.

Step4: Check Option C

Set $x=0$: $3(0)-8y=-5 \implies -8y=-5 \implies y=\frac{5}{8}$, not $-8$.

Step5: Check Option D

Set $x=0$: $-8(0)+3y=-5 \implies 3y=-5 \implies y=-\frac{5}{3}$, not $-8$.

Answer:

A. $y = 3x - 8$