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Let line $t$ be the line represented by $3x+4y = 5$ and let line $p$ be the line perpendicular to line $t$ and containing the point $(5,5)$. What is the $x$-coordinate of the point common to line $t$ and line $p$? Express your answer as a common fraction.

Guest Dec 7, 2017

#1**+2 **

$3x+4y = 5 ⇒ y = (-3/4)x + 5/4 (1)

The slope of this line = -3/4

So....the slope of a perpendicular line = 4/3

And the equation of thiis line is

y = (4/3)(x - 5) + 5

y = (4/3)x - 20/3 + 5

y = (4/3)x -5/3 (2)

Setting (1) and (2) equal, we have that

(-3/4)x + 5/4 = (4/3)x - 5/3 multiply through by 12

-9x + 15 = 16x - 20 add 20, 9x to both sides

35 = 25x divide both sides by 25

35/25 = 7/5 = x

CPhill Dec 7, 2017