_{L2 }= -3

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

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

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

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 m_{p} = -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 m_{p} = -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

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