Question

Write the equation of the line that passes through the point (3,4) and is perpendicular to the line y=-2x-4.

Answer 1

Answer:

y = $\frac{1}{2}$ x + $\frac{5}{2}$

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 - 4 ← 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

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

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

To find c substitute (3, 4) into the partial equation

4 = $\frac{3}{2}$ + c ⇒ c = 4 - $\frac{3}{2}$ = $\frac{5}{2}$

y = $\frac{1}{2}$ x + $\frac{5}{2}$ ← equation of line