Question

Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form.

perpendicular to
7y = x − 4
and passes through the point
(−2, 1)

Answer 1

`y = -7x -13`

Explanation:

Given

Perpendicular to

`7y = x -4`

Passes through

`(-2,1)`

Required

The equation

First, we calculate the slope of:

`7y = x -4`

Divide through by 7

`y = (1)/(7)x - (4)/(7)`

A linear function is:

`y=mx + c`

Where;

`m \to slope`

So:

`m = (1)/(7)`

For the perpendicular line; the slope is:

`m_2 = -(1)/(m)`

So, we have:

`m_2 = -(1)/(1/7)`

`m_2 = -7`

The equation is:

`y = m(x - x_1) + y_1`

So, we have:

`y = -7(x - -2) + 1`

`y = -7(x +2) + 1`

Open bracket

`y = -7x -14 + 1`

`y = -7x -13`