Answer:
y = 3x - 17
Step-by-step explanation:
the equation of a line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
given the line with equation
y = - [tex]\frac{1}{3}[/tex] x + 2 ← in slope- intercept form
with slope m = - [tex]\frac{1}{3}[/tex]
given a line with slope m, then the slope of a line perpendiclar to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{3} }[/tex] = 3 , then
y = 3x + c ← is the partial equation
to find c, substitute (5, - 2 ) for x and y in the partial equation
- 2 = 3(5) + c = 15 + c ( subtract 15 from both sides )
- 17 = c
y = 3x - 17 ← equation of perpendicular line
