Question

(person who helps gets medal)
Find the equation of a line that passes through the point (4,2) that is perpendicular to the line y = x. Show your work.

Answer 1

\[y = \frac{ 4 }{ 3 } X\]

Answer 2

is that your answer?

Answer 3

no the fraction did not appear when I copy and paste

Answer 4

the 4/3 is suppose to be in the question

Answer 5

so what would the slope be of a line that is perpendicular to y=3/4x?

Answer 6

How do we find that?

Answer 7

mmm im having trouble since its a fraction ~

Answer 8

do i put it like this

y2 - y1
--------
x2 - x1

Answer 9

If one line has a slope of \(\frac{1}{2}\), then the line that is perpendicular to it will be the negative reciprocal \(-2\)

Answer 10

nope to find the slope of a line that is perpendicular to that, you just do the opposite reciprocal of the slope of y=3/4x

Answer 11

so i make it negative ?

3 / 4 - ?

Answer 12

and reciprocal

Answer 13

??

Answer 14

@Vocaloid

Answer 15

Yes, so now we have our new slope.

Now we must plug in the other values that we're given. We're told that the line runs through the point (4, 2)

Equation of a Line:
\[\large (y-y_1)=m(x-x_1)\]

Answer 16

Plug in the point into \(y_1\) and \(x_1\) and our slope \(m\) that we just also found.

Answer 17

\[(y - 2) = -\frac{ 3 }{ 4 }( x - 4)\]

Answer 18

this ?

Answer 19

Yep! X)

Now simplify. So distribute the (-3/4) and then add 2 to both sides.

Answer 20

how would u distribute the -3/4 ?

Answer 21

@CShrix

Answer 22

Let's look at 2(x+1)
By distributing, we multiply each term by 2
so 2(x+1) = 2x+2

Answer 23

sooo you multiply the fraction by x and 4 ?

Answer 24

could you draw it out instead of saying it? i can under stand it so much better

Answer 25

We have to multiply x and (-4) by (-3/4)

Answer 26

so it would be -3/4x - 12/3 ?

Answer 27

?

Answer 28

(3/4)(4) is not (12/3)

Answer 29

what is it then ~

Answer 30

im super bad at fractions

Answer 31

\[y-2=-\frac{3}{4}x+\frac{12}{4}\]

Answer 32

thats the answer ?

Answer 33

Actually it depends on which form they want. If they want it in `slope-intercept `form, then we must add both sides by 2 to isolate y.

But if they want the answer in `point-slope` form, then our answer is just
\(\large (y - 2) = -\frac{ 3 }{ 4 }( x - 4)\)

If it doesn't specify, then I would just leave it in point-slope form, which we already have.

Answer 34

ok so yes alright thank you ! :)

Answer 35

You are welcome :)