Question

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

The point-slope form of the line that passes through (5,5) and is perpendicular to a line with a slope of
`(1)/(4)` is 4x + y -25 = 0

Solution:

The point slope form of the line that passes through the points
`\left(x_(1) y_(1)\right)` and perpendicular to the line with a slope of “m” is given as

`\bold{y-y_(1)=-(1)/(m)\left(x-x_(1)\right)}` ---- eqn 1

Where “m” is the slope of the line.
`x_(1) \text { and } y_(1)` are the points that passes through the line.

From question, given that slope “m” =
`(1)/(4)`

Given that the line passes through the points (5,5).Hence we get

`x_(1)=5 ; y_(1)=5`

By substituting the values in eqn 1 , we get the point slope form of the line which is perpendicular to the line having slope
`(1)/(4)`can be found out.

y - 5 = -4(x - 5)

y - 5 = -4x + 20

on simplifying the above equation, we get

y - 5 + 4x -20 = 0

4x + y - 25 = 0

hence the point slope form of given line is 4x + y - 25 = 0