Hi how do i , Find the equation of the line in slope intercept form that is perpendicular to the line 2x - 8y + 20 = 0 that goes through the point (-1, 6)

Question

asked Nov 24, 2023 138k views

1 Answer

Kindra · Answer 1 · 2023-12-01T17:48:32+0000

We have the following equation:

In order to locate the slope of this line equation, lets isolate the variable y. Then, by subtracting 2x and 20 to both sides, we have

and by dividing both sides by -8, we obtain

$\begin{gathered} y=(-2x-20)/(-8) \\ y=-(2)/(-8)x-(20)/(-8) \\ y=(1)/(4)x+(5)/(2) \end{gathered}$

By comparing this result with the slope-intercept form

we can see that the slope m of the given line equation is

Since we need a perperdicular line, we need to compute the negative reciprocal of the slope m, that is,

$\begin{gathered} M\questeq-(1)/(m) \\ so \\ M=-(1)/((1)/(4))=-4 \end{gathered}$

Then, the perpendicular line has the form

$\begin{gathered} y=Mx+b \\ \text{that is, } \\ y=-4x+b \end{gathered}$

Finally, we can find the y-intercept b by substituting the coordinates of the given point (-1,6). It yields,

which gives

$\begin{gathered} 6=4+b \\ \text{then} \\ b=2 \end{gathered}$

Therefore, the perpendicular line to 2x-8y+20=0 that goes throught the point (-1,6) is: