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# Equations of Lines

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What is the equation of a line that passes through the point (-7,2) and is perpendicular to the line whose equation is y = −2/5*x + 8?

Apr 17, 2021

#1
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The slope of our line y = x/4 + 5 is m = 1/4

Since we're coming up with the equation of a line that is perpendicular, the slope of our perpendicular line is the opposite reciprocal of 1/4, or m = - 4/1 or m = 4

Now, we need to find out the y-intercept of our perpendicular line. To do that we plug in (2, 7) into x and y as well as - 4 into m in the following equation:

y = mx + b

7 = (- 4)(2) + b

7 = - 8 + b

15 = b

Thus, with m = - 4 and b = 15, the equation of our perpendicular line is:

y = - 4x + 15

WARNING: Possibly wrong~ Hannah

Apr 17, 2021
#2
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Slope of given line  is m = -2/5     perpindicular is  - 1/m = 5/2

Point slope form of the new line through -7, 2    is      y-2   = 5/2 ( x - -7)

y = 5/2 x + 35/2 +2

y = 5/2 x + 39/2

Here is a graph ( which I used as a check):

https://www.desmos.com/calculator/kvm5df9b2n

Apr 17, 2021
#4
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Thanks for checking :/ ~Hannah

Guest Apr 17, 2021