Question

Find the equation of the line perpendicular to y=2x-6 that passes through the point (1,5). If possible, write the equation in slope-intercept form.

Answer 1

Answer:

y = - $\frac{1}{2}$ x + $\frac{11}{2}$

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 = 2x - 6 ← is in slope- intercept form

with slope m = 2

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{2}$ , thus

y = - $\frac{1}{2}$ x + c ← is the partial equation

To find c substitute (1, 5) into the partial equation

5 = - $\frac{1}{2}$ + c ⇒ c = 5 + $\frac{1}{2}$ = $\frac{11}{2}$

y = - $\frac{1}{2}$ x + $\frac{11}{2}$ ← equation of perpendicular line