Question

Write the point-slope form of the line that passes through (5,5) and is parallel 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 parallel to a line with a slope of $\frac{1}{4}$ is x -4y +15 = 0

Solution:

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

$\bold{y-y_{1} = m\left(x-x_{1}\right)}$ --- 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 parallel to the line having slope $\frac{1}{4}$ can be found out.

$y-5=\frac{1}{4}(x-5)$

On cross multiplying we get

4y – 20 = x – 5

On rearranging, we get

x-5-4y+20 = 0

x – 4y +15 = 0

hence the point slope form the given line is x – 4y +15 = 0