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write an equation of the line that is perpendicular to 3x - 4y equals 9 + contains (-4, -5)

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GoddessofDork
  • Slope-Intercept Form: y = mx+b, with m = slope and b = y-intercept

So perpendicular lines have slopes that are negative reciprocals to each other, but firstly we need to find the slope of the original equation. The easiest method to find it is to convert this standard form into slope-intercept.

Firstly, subtract 3x on both sides of the equation: [tex] -4y=-3x+9 [/tex]

Next, divide both sides by -4 and your slope-intercept form of the original equation is [tex] y=\frac{3}{4}x-\frac{9}{4} [/tex]

Now looking at this equation, we see that the slope is 3/4. Now since our new line is perpendicular, this means that its slope is -4/3.

Now that we have the slope, plug that into the m variable and plug in (-4,-5) into the x and y coordinates to solve for the b variable as such:

[tex] -5=-\frac{4}{3}*-4+b\\\\-5=5\frac{1}{3}+b\\\\-10\frac{1}{3}=b [/tex]

In short, your new equation is y = -4/3x - 10 1/3.
3x-4y=9
-4y=-3x+9
y=3x/4 -9/4

To get the perpendicular equation, first you have to find the find the opposite reciprocal of the slope.

y= -4x/3 +___

Now, when you've found the slope, you multiply it by the x value, and find the difference between that and the y value.

-4/3(-4)
16/3 -(-5)
10/3

Since you have to subtract 16/3, you out a negative on the 10/3

y= -4x/3 -10/3 should be your answer.