Question

a line has a slope of $-\frac{1}{2}$ and passes through the point $(3, -2)$. write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m =-\frac{1}{2}$ and $(x_1,y_1)=(3,-2)$.
Substitute these values into the point - slope form: $y-(-2)=-\frac{1}{2}(x - 3)$
Simplify the left - hand side: $y + 2=-\frac{1}{2}(x - 3)$

Step2: Convert to slope - intercept form ($y=mx + b$)

First, distribute the $-\frac{1}{2}$ on the right - hand side:
$y+2=-\frac{1}{2}x+\frac{3}{2}$
Then, subtract 2 from both sides to solve for $y$. We know that $2=\frac{4}{2}$, so:
$y=-\frac{1}{2}x+\frac{3}{2}-\frac{4}{2}$
Simplify the right - hand side:
$y=-\frac{1}{2}x-\frac{1}{2}$

Answer:

$y = -\frac{1}{2}x-\frac{1}{2}$