Question

m = \frac{1}{2}
(-6, 12)

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $m = \frac{1}{2}$, $x_1=-6$ and $y_1 = 12$.

Step2: Substitute values into point - slope form

Substitute $m=\frac{1}{2}$, $x_1=-6$ and $y_1 = 12$ into the point - slope formula:
$y-12=\frac{1}{2}(x - (-6))$
Simplify the right - hand side: $y - 12=\frac{1}{2}(x + 6)$

Step3: Convert to slope - intercept form (optional, if we want to find the equation in $y=mx + b$ form)

Distribute $\frac{1}{2}$ on the right - hand side: $y-12=\frac{1}{2}x+3$
Add 12 to both sides: $y=\frac{1}{2}x+3 + 12$
Simplify: $y=\frac{1}{2}x+15$

If the problem was to find the equation of the line with slope $m = \frac{1}{2}$ passing through the point $(-6,12)$, the equation is $y=\frac{1}{2}x + 15$ (or in point - slope form $y - 12=\frac{1}{2}(x + 6)$)

Answer:

If the goal is to find the equation of the line, the slope - intercept form is $y=\frac{1}{2}x + 15$ and the point - slope form is $y - 12=\frac{1}{2}(x+6)$