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# points help

Find the slope-intercept equation of the line perpendicular to the line x - 3y = 4 and containing the point (6,-9). Explain/show work.

### 2 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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L1 : X - 3Y = 4

Y = X/3 + 4/3

L2  l  L1

m L2 = -3

L2 :   Y = -3X +b

Passes through ( 6 , -9) , then:

- 9 = -3( 6 ) +b

b = -9 + 18 = 9

L 2 :   Y = -3X + 9
Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
4.9 4.9 (418 lesson ratings) (418)
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### Find the slope-intercept equation of the line perpendicular to the line x - 3y = 4 and containing the point (6,-9).

First, let's rewrite the equation in standard slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:

x-3y = 4
-3y = 4 - x               (Subtract x from both sides)
y = (1/3)x -4           (Divide both sides by -3)

The slope of this line is m = 1/3.  If the slope of a line is m, the slope of the line perpendicular to it is -1/m.  So the slope of a line that's perpendicular to y = (1/3)x - 4 is mp = -1/(1/3) = -3.

OK, we're half way there.  We want to find the formula of line perpendicular to y = (1/3)x - 4.  We know it will have a slope mp = -3 and the line passes through the point (6,-9)
y = (-3)x + b
-9 = (-3)(6) + b        (Plug in -9 for y, 6 for x)
-9 = -18 + b
9 = b                        (Solve for b)

So our equation is:

y = -3x + 9