Question

2 what is the y-intercept of each equation?
a. $y = 6x + 2$
b. $10x + 5y = 30$
c. $y - 6 = 2(3x - 4)$

Explanation:

Step1: Identify slope-intercept form

The y-intercept is the value of $y$ when $x=0$, or the constant term in $y=mx+b$ (where $b$ is the y-intercept).

Step2: Solve for part a

Equation is already in $y=mx+b$: $y=6x+2$. Here, $b=2$.

Step3: Solve for part b

Set $x=0$ in $10x+5y=30$:
$10(0)+5y=30$
$5y=30$
$y=\frac{30}{5}=6$

Step4: Solve for part c

First rewrite in slope-intercept form:
$y-6=2(3x-4)$
$y-6=6x-8$
$y=6x-8+6$
$y=6x-2$
The constant term $b=-2$.

Answer:

a. 2
b. 6
c. -2