Question

Which of the following equations contains the point (8,5) and is perpendicular to the line y=2x-3

Answer 1

Answer:

y = - $\frac{1}{2}$ x + 9

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 - 3 ← 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 (8, 5) into the partial equation

5 = - 4 + c ⇒ c = 5 + 4 = 9

y = - $\frac{1}{2}$ x + 9 ← equation of line