Answer:
x + 19y = 117
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 )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, 2) and (x₂, y₂ ) = (6, 21)
m = [tex]\frac{21-2}{6-5}[/tex] = 19
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}{19}[/tex] , thus
y = - [tex]\frac{1}{19}[/tex] x + c ← is the partial equation
To find c substitute (3, 6) into the partial equation
6 = - [tex]\frac{3}{19}[/tex] + c ⇒ c = 6 + [tex]\frac{3}{19}[/tex] = [tex]\frac{117}{19}[/tex]
y = - [tex]\frac{1}{19}[/tex] x + [tex]\frac{117}{19}[/tex] ← equation in slope- intercept form
Multiply through by 19
19y = - x + 117 ( add x to both sides )
x + 19y = 117 ← equation in standard form
