Answer
Point-slope form $y-4=-3(x−2)$ or $y+2=-3(x−4)$.
Slope-intercept form $ y=-3x+10$ or $ f(x)=-3x+10$.
Work Step by Step
If the line passes through a point $(x_1,y_1)$ and slope is $m$ then point-slope form is.
$\Rightarrow y−y_1=m(x−x_1)$
From the question we have
$\Rightarrow (x_1,y_1)=(2,4)$
$\Rightarrow (x_2,y_2)=(4,-2)$
Slope $m=\frac{change\;in\; y}{change\;in\; x}$
$\Rightarrow m=\frac{y_2−y_1}{x_2−x_1}$
Substitute all values.
$m=\frac{-2−4}{4−2}$
$m=\frac{-6}{2}$
$m=-3$
For the first point $(x_1,y_1)=(2,4)$
Substitute all values into the equation.
$\Rightarrow y−4=(-3)(x−2)$
Simplify.
$\Rightarrow y−4=-3(x−2)$
The above equation is the point-slope form.
For the second point $(x_2,y_2)=(4,-2)$
Substitute all values into the equation.
$\Rightarrow y−(-2)=-3(x−4)$
Simplify.
$\Rightarrow y+2=-3(x−4)$
The above equation is the point-slope form.
Solve the equation for $y$.
$\Rightarrow y+2=-3(x−4)$
Use distributive property.
$\Rightarrow y+2=-3x+12$
Add $-2$ to both sides.
$\Rightarrow y+2-2=-3x+12-2$
Simplify.
$\Rightarrow y=-3x+10$
The above equation is the slope-intercept form.
