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=-(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=-(1)/(4)x+3`

Here, the slope of the line is
`-(1)/(4)`.

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

`-(1)/(4)* 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`.