Question

Please help
Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through the point (6, 3).
y = 2x + 6
y = −one half x + 3
y = −one half x + 6
y = 2x + 3

Answer 1

Do you remember the previous problem?
The first step is to find the slope of the given equation.
Compare
\( y = 2x + 2 \) to
\(y = mx + b\)
What is the slope of the given line?

Answer 2

2 is the slope

Answer 3

Great.
In the previous problem we need a parallel line. Parallel lines hav the sam e slope.

In this problem we need a perpendicular line. Perpendicular lines have slopes that are "negative reciprocals."

All that means is that if you know the slope of a line, to find the slope of a perpendicular, write the slope of the given line as a fraction. Then flip the fraction (reciprocal) then change the sign (negative.)

Answer 4

We know our line has a slope of 2.

Let's find the slope of the perpendicular:
1. Write 2 as a fraction.

Answer 5

It will be the second or third one.. right?

Answer 6

Correct. It has to be one of those two, since the negative reciprocal of 2 is \( -\dfrac{1}{2} \).

Answer 7

Is it C

Answer 8

Crap I only have 2 minutes left on my test.

Answer 9

Now we know the perpendicular line has to be:

\(y = -\dfrac{1}{2}x + b\)

We need b. We do the same we did in the last problem.

Input the x and y of the given point into

\(y = -\dfrac{1}{2}x + b\)

and solve for b.

\(3 = -\dfrac{1}{2}(6) + b\)

\(3 = -3 + b\)

\(6 = b\)

Since we have \(b = 6\) we then have:

\(y = -\dfrac{1}{2}x + 6\)

Answer 10

YES I WAS CORRECT

Answer 11

Great.

Answer 12

Thank you so much, you were such a hug hel[

Answer 13

*huge help

Answer 14

ty for medal

Answer 15

Thanks. You're welcome.