Answer
Point-slope form: $y-6=2(x-1)$ or $y-2=2(x+1)$.
Slope-intercept form: $y=2x+4$.
Work Step by Step
If the line passes through a point $(x_1,y_1)$ and slope is $m$, then the point-slope form of the line's equation is.
$\Rightarrow y-y_1=m(x-x_1)$.... (1)
We are given:
$\Rightarrow (x_1,y_1)=(1,6)$
$\Rightarrow (x_2,y_2)=(-1,2)$
Slope $m=\frac{change\;in\;y}{change\;in\;x}$
$\Rightarrow m=\frac{y_2-y_1}{x_2-x_1}$
Substitute all values.
$\Rightarrow m=\frac{2-6}{-1-1}$
$\Rightarrow m=\frac{-4}{-2}$
$\Rightarrow m=2$
For the first point $(x_1,y_1)=(1,6)$
Substitute all values into the equation (1).
$\Rightarrow y-(6)=(2)(x-(1))$
Simplify.
$\Rightarrow y-6=2(x-1)$
The above equation is the point-slope form.
For the second point $(x_2,y_2)=(-1,2)$
Substitute all values into the equation (1).
$\Rightarrow y-(2)=(2)(x-(-1))$
Simplify.
$\Rightarrow y-2=2(x+1)$
The above equation is the point-slope form.
Now isolate $y$ to determine the slope-intercept form:
$y=mx+b$.
Use the distributive property.
$\Rightarrow y-2=2x+2$
Add $2$ to both sides.
$\Rightarrow y-2+2=2x+2+2$
Simplify.
$\Rightarrow y=2x+4$
The above equation is the slope-intercept form.
