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nirvana33 [79]
3 years ago
7

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

Mathematics
2 answers:
Eva8 [605]3 years ago
8 0
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.
Inga [223]3 years ago
3 0
  • Slope-Intercept Form: y = mx+b, with m = slope and b = y-intercept

So perpendicular lines have <u>slopes that are negative reciprocals</u> 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: -4y=-3x+9

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

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

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:

-5=-\frac{4}{3}*-4+b\\\\-5=5\frac{1}{3}+b\\\\-10\frac{1}{3}=b

<u>In short, your new equation is y = -4/3x - 10 1/3.</u>

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