Answer:
y = 4x + 3
Step-by-step explanation:
Calculate the slope m of the given line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 3) and (x₂, y₂ ) = (4, 1) ← 2 points on the line
m = [tex]\frac{1-3}{4-(-4)}[/tex] = [tex]\frac{-2}{4+4}[/tex] = [tex]\frac{-2}{8}[/tex] = - [tex]\frac{1}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{4} }[/tex] = 4
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
The line crosses the y- axis at (0, 3) ⇒ c = 3
y = 4x + 3 ← equation of perpendicular line
