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

Answer:

The point-slope form of the line that passes through (5,5) and is perpendicular to a line with a slope of $\frac{1}{4}$ 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  

$\bold{y-y_{1}=-\frac{1}{m}\left(x-x_{1}\right)}$ ---- 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” = $\frac{1}{4}$

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 $\frac{1}{4}$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