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Question

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

Answer 1

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 

Answer 2

Hello, thank you for taking the time to post your question!

For slope-intercept form you want to put y = mx + b, where “m” is the slope and “b” is the y-intercept. In this question you’re given that the slope of the perpendicular line is 1/3, meaning that the slope that we’re trying to find is going to be m = -3. From there then I would plug in the point (6, -9) and slope into the equation to solve

y – (-9) = -3(x – 6)

y + 9 = -3x + 18

y = -3x + 9

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 3

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 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