Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given y = 5(x + 1) = 5x + 5 ← in slope- intercept form
with slope m = 5
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}{5}[/tex], thus
y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (10, 2) into the partial equation
2 = - 2 + c ⇒ c = - 2 + 2 = 4
y = - [tex]\frac{1}{5}[/tex] x + 4 ← in slope intercept form
Multiply all terms by 5
5y = - x + 20 ( add x to both sides )
x + 5y = 20 ← in standard form → D
