Question

Write an equation in slope-intercept form for the line that passes through (0, –2) and is perpendicular to the graph of y = −¼ x + 3

Answer 1

Given:

A line passes through the point (0,2) and is perpendicular to the graph of $y=-\dfrac{1}{4}x+3$.

To find:

The slope intercept form of the given line.

Solution:

Slope intercept form of a line is

$y=mx+b$

Where, m is slope and b is y-intercept.

We have,

$y=-\dfrac{1}{4}x+3$

Here, the slope of the line is $-\dfrac{1}{4}$.

The product of slopes of two perpendicular lines is -1.

$-\dfrac{1}{4}\times m=-1$

$m=4$

The slope of the required line is m=4 and it passes through the point (0,2). So, the equation of the required line is

$y-y_1=m(x-x_1)$

$y-2=4(x-0)$

$y-2=4x$

$y=4x+2$

Therefore, the equation of the required line is $y=4x+2$.