Find the slope‐intercept equation of the line with the following properties:Perpendicular to the line x-4y=2; containing the point (5,2).

Expert Answers
lfryerda eNotes educator| Certified Educator

The slope-intercept form of a line is written as `y=mx+b` where m is the slope and b is the y-intercept.  To find this equation, we need the slope of the line and any point on the line.  We have the point, it is (5,2).  The slope is perpendicular to the line:

 `x-4y=2`  rearrange

`-4y=-x+2`   divide by -4

`y=1/4 x-2/4`   

which has slope `1/4` .  A line perpendicular to this one has a slope that is the negative reciprocal, which has slope -4.

This means the line we are looking for has slope -4 and goes through the point (5,2).

Sub into the equation of the line:


`2=-4(5)+b`   solve for b



This means the equation of the line is `y=-4x+22` .

ms718 | Student

Thanks so very much I understand