Question

find the slope and the y-intercept of the line.
-3x - 4y = -8
write your answers in simplest form.
slope:

y-intercept:

Explanation:

Step1: Rewrite in slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. We start with the equation $-3x-4y=-8$. First, we want to solve for $y$.
Add $3x$ to both sides of the equation:
$-4y = 3x - 8$

Step2: Solve for y

Divide every term in the equation $-4y=3x - 8$ by $-4$:
$y=\frac{3x}{-4}+\frac{-8}{-4}$
Simplify each term:
$y =-\frac{3}{4}x + 2$

Step3: Identify slope and y - intercept

From the equation $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. Comparing $y =-\frac{3}{4}x + 2$ with $y=mx + b$, we can see that the slope $m =-\frac{3}{4}$ and the $y$-intercept $b = 2$.

Answer:

slope: $-\frac{3}{4}$
y - intercept: $2$