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determine the equation of the line that is perpendicular to the line y= -3/4 x - 7 that passes through (5,-6)

User Chrisvj
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2 Answers

2 votes

Answer:

y=4/3x-38/3

Explanation:

Equation: y=-3/4x-7

Change the reciprocal (x-value):

In order to change the reciprocal you must change the sign from negative to positive

-3/4 ---> 3/4

Then you must flip the fraction.

3/4 ---> 4/3

Adding in the given coordinates:

We must use the given coordinate in order to find the new y-intercept because '-7' is part of the perpendicular line of the new line we are creating.

In order to add in the given coordinates you must use 'y-y1=m(x-x1)' to get your new y-intercept.

The 'y' stays as 'y'

The 'y1' is the y-value of your coordinate

The 'm' is your new slope

The 'x' stays as 'x'

The 'x1' is the x-value of your coordinate

Coordinate Given: (5,-6) New Slope: 4/3

y-(-6)=(4/3)(x-(5))

To solve you must get 'y' by itself, so lets work on 'y-(-6)'.

A negative and a negative make a positive.

y-(-6) ---> y+6

Now let's work on '(4/3)(x-(5))'.

You must distribute in the 4/3

(4/3)(x) ---> 4/3x

(4/3)(-5) ---> -20/3

Now you have 'y+6=4/3x-20/3'

Now solve to get 'y' by itself by subtracting 6 on both sides.

y+6 -6 ---> y (the 6's cancel out)

4/3x-20/3 -6 ---> 4/3x-38/3 (You only subtract the same number and since there was no 'x' you can only subtract 6 from (-20/3))

So now you have your new line that is perpendicular to your first line

New Equation: y=4/3x-38/3

User Sophiane
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7.7k points
5 votes
y= 4/3x-12 2/3 is a perpendicular line that passes through (5,-6)
User Brijesh Lakkad
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8.5k points

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