Question

An equation of a line through (0,2) which is perpendicular to the line y=4x+4 has slope and y-intercept

Answer 1

Answer:

Slope of the line is -1/4 and y intercept is 2.

Step-by-step explanation:

Let the equation of the required line be given as $\[y=mx+c\]$

The required line is perpendicular to the line $\[y=4x+4\]$

Slope of the line $\[y=4x+4\]$ is 4.

$\[=> m*4 = -1\]$

$\[=> m = \frac{-1}{4}\]$

So the equation of the line becomes:

$\[y=\frac{-1}{4}x+c\]$

But this line passes through the point (0,2).

$\[=>2=\frac{-1}{4}*0+c\]$

$\[=>c=2\]$

So the equation of the line is :

$\[y=\frac{-1}{4}x+2\]$

Its slope is -1/4 and y intercept is 2.