Question

1.) Two perpendicular lines intersect at the origin. If the slope of the first line is -1/2, what is the equation of the second line?

2.)The slope of a line is -1/2 What is the slope of a line that is parallel to it?

3.)What is the equation of the line that passes through the points (1,2/3) and (-1,-1)

Answer 1

@diamondprincess @nicolehill @iGreen

Answer 2

Perpendicular lines have opposite slope..what's the opposite of -1/2? @RosePetal_

Answer 3

consider two lines
\[y=m_x+b\\and\\y=m_2x+c\\they~will~be~perpendicular~when\\\boxed {m_1*m_2=-1}\]

Answer 4

Wait which number is this for? and opposite of -1/2 is 1/2

Answer 5

no perpendicular lines does'nt have only opposite but also negetive slope

Answer 6

i think i know the answer to number 2 but I'm not completely sure

Answer 7

No, switch 1/2 around what do you get? @RosePetal_

Answer 8

2

Answer 9

so for the first line slope
\[m_1=-1/2\]
then slope of the line perpendicular to it will be
\[m_2=\frac{ -1 }{ m_1 }=\frac{ -1 }{ 1-/2 }=2\]
got it?
yes good

Answer 10

Yep, so that's the slope of the 2nd line for #1.

Answer 11

For #2:

Parallel lines have the same slope..so what's the slope of line 2 gonna be?

Answer 12

oh okay so for number one you just switch it around

Answer 13

Yep, and you change it to positive..

Answer 14

wouldn't it be -2

Answer 15

now u need the equation for the perpendicular line ok?

Answer 16

2.)The slope of a line is -1/2 What is the slope of a line that is parallel to it?

Parallel lines have the SAME slope. So what's the slope of the line parallel to the original? @RosePetal_

Answer 17

so equation for the perpendicular line is\[y=2x\]

Answer 18

2??

Answer 19

and real fast 2 isn't an answer for number 1 i attached a pic of the answers I'm stuck between a and d

Answer 20

No, 2 is incorrect.

Slope of line #1 = -1/2

Slope of line #2 is parallel to line #1.

parallel lines have the same slope.

Answer 21

oh I'm an idiot so it would be -1/2

Answer 22

2 is the slope of the line for #1..and there's only one answer with 2 in it..

Answer 23

Yep, the slope for line #2 will also be -1/2..

Answer 24

okay sorry I'm not thinking right now a haha and then what about number 3

Answer 25

for #3 first calculate slope

Answer 26

can u do that?

Answer 27

slope=y2-y1/x2-x1

Answer 28

Equation for slope:

\(m = \dfrac{y_2-y_1}{x_2-x_1}\)

Our points are (1, 0.67) and (-1, -1)

Plug them in:

\(m = \dfrac{-1-0.67}{-1-1}\)

Subtract:

\(m = \dfrac{-1.67}{-2}\)

Can you divide that? @RosePetal_

Answer 29

ya it would be .835

Answer 30

yes which is equal to 5/6

Answer 31

so the answer to number 3 is 5/6x-1/6

Answer 32

Yep, so slope is 5/6..

Answer 33

now when u have the slope then use
\[y-y_1=m(x-x_1)\]
this form to calculate equation of the line :)

Answer 34

another quick question i just wanna double check my answer - Rewrite the slope-intercept form equation into standard form.
y = –2x + 4
would the answer be 2x + y = 4

Answer 35

yes!

Answer 36

Standard form is Ax + By = C.

Answer 37

So that would be correct. @RosePetal_

Answer 38

Yas!!! Thanxx so much