SOLUTION: f(x)=-2/3(x) + 1/2 Write the equation of a line perpendicular to f that passes through the point (2, 1). The functions is negative two thirds and the variable is x plus one

Question 1173961: f(x)=-2/3(x) + 1/2
Write the equation of a line perpendicular to f that passes through the point (2, 1).
The functions is negative two thirds and the variable is x plus one half.
I'd appreciate a detailed procedure of this because what I really need to do is to is to write a step by step kind of the problem.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

The given function is which is the same as since y = f(x).

This equation is in the form y = mx+b with
m = -2/3 = slope
b = 1/2 = y intercept

We won't use this given y intercept. We'll only use the slope.

The negative reciprocal of the given slope is 3/2. We flip the fraction to go from -2/3 to -3/2. We also flip the sign from negative to positive.

Side note: The original slope -2/3 and the perpendicular slope 3/2 multiply to -1. This works for any pair of perpendicular lines as long as neither line is vertical.

So far we found the perpendicular slope to be m = 3/2

We want this perpendicular line to go through (x,y) = (2,1)

We will use
m = 3/2
x = 2
y = 1
to plug into y = mx+b. Then we'll solve for b

So,
y = mx+b
1 = (3/2)*2+b
1 = 3+b
1-3 = b
-2 = b
b = -2

This means y = mx+b updates to to be the equation of the perpendicular line.

If you wish to use point-slope form, then you could do it like this

------------------------------------

Answer:

Because 3/2 = 1.5, the decimal form of this equation is

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