Question

which equation represents the line that contains the point (3, -6) and has a slope of $\frac{1}{2}$?
$y + 3=\frac{1}{2}(x - 6)$
$y - 3=\frac{1}{2}(x + 6)$
$y + 6=\frac{1}{2}(x - 3)$
$y - 6=\frac{1}{2}(x + 3)$

Explanation:

Step1: Recall point - slope formula

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Identify values of $x_1$, $y_1$ and $m$

Given the point $(3,-6)$ and slope $m = \frac{1}{2}$, so $x_1 = 3$ and $y_1=-6$.

Step3: Substitute values into formula

Substitute $x_1 = 3$, $y_1=-6$ and $m=\frac{1}{2}$ into $y - y_1=m(x - x_1)$. We get $y-(-6)=\frac{1}{2}(x - 3)$, which simplifies to $y + 6=\frac{1}{2}(x - 3)$.

Answer:

$y + 6=\frac{1}{2}(x - 3)$ (the third option)