Question

Need HELP!!!! Write the point-slope form of the line that passes through (5, 5) and is perpendicular to a line with a slope of 1/4. Include all of your work in your final answer.

Answer 1

`y - 5 = -4(x-5)`

Explanation:

Given

Line coordinates: (5,5)

Perpendicular slope =
`(1)/(4)`

Required

Find the point slope form of the line

First, the slope of the line has t be calculated;

Given that two lines are perpendicular;

The relationship between there slopes is given as
`m_1.m_2 = -1`

Let m_2 represent the slope of the second line;

such that
`m_2 = (1)/(4)`

So;

`m_1 * (1)/(4) = -1`

Multiply both sides by 4

`m_1 * (1)/(4) * 4 = -1 * 4`

`m_1 = -1 * 4`

`m_1 = -4`

Now, the equation of the line can be calculated using slope formula;

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

Where

`(x_1,y_1) = (5,5)\\m_1 =m = -4`

So;
`m = (y - y_1)/(x- x_1)` becomes

`-4 = (y - 5)/(x- 5)`

Multiply both sides by x - 5

`-4(x-5) = (y - 5)/(x- 5) * (x-5)`

`-4(x-5) = y - 5`

Reorder

`y - 5 = -4(x-5)`

Hence, the line in point-slope form is
`y - 5 = -4(x-5)`