Question

What is the equation of a line that passes through the point (10, 5) and is perpendicular to the line whose equation is y=5/4x−2 ?

Answer 1

`\displaystyle 4x + 5y = 65\:or\:y = -(4)/(5)x + 13`

Explanation:

5 = −⅘[10] + b

−8

`\displaystyle 13 = b \\ \\ y = -(4)/(5)x + 13`

If you want it in Standard Form:

y = −⅘x + 13

+ ⅘x + ⅘x

___________

⅘x + y = 13 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

5[⅘x + y = 13]

`\displaystyle 4x + 5y = 65`

* Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES], so 1¼ [or 5⁄4] becomes −⅘.

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