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Im having trouble with my homework and im not sure how to do this question could someone please explain?

line u has an equation of y+6=3/2(x–6). Line v is perpendicular to line u and passes through (2,–1). What is the equation of line v?

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First write out the equation. Use distributive property for 3/2(x-6) by multiplying 3/2 by x and by -6. Then, subtract 6 from both sides and add -6 and the -18/2 from the previous distributive property step.
y= 3/2x -15
To find the perpendicular line, you need to change the slope (which is 3/2) to its negative reciprocal.
In order to do that, flip the order to 2/3 and multiply it by negative 1 to get -2/3.
y = -2/3x + b
You still can’t fully write out the equation because you don’t know b, which is the y intercept. To find it, plug in the x and y of (2,-1) to y = -2/3x + b.
-1 = -4/3 + b

Next move 4/3 to the left by adding it to both sides.
1/3 = b (aka y intercept)
Then you can write the final equation of line v.
y = -2/3x + 1/3

Not super sure if it’s correct, but I hope it helped!
User Terence Golla
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