Question

Which equation represents the line that is perpendicular to y=3/4x+1 and passes through (-5,11)

Answer 1

Answer:

y = - $\frac{4}{3}$ x + $\frac{13}{3}$

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 )

y = $\frac{3}{4}$ x + 1 ← is in slope- intercept form

with slope m = $\frac{3}{4}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{3}{4} }$ = - $\frac{4}{3}$ , thus

y = - $\frac{4}{3}$ x + c ← is the partial equation

To find c substitute (- 5, 11) into the partial equation

11 = $\frac{20}{3}$ + c ⇒ c = 11 - $\frac{20}{3}$ = $\frac{13}{3}$

y = - $\frac{4}{3}$ x + $\frac{13}{3}$ ← equation of perpendicular line