Question

Write an equation of a line perpendicular to line CD below in slope-intercept form that passes through the point (−1, 6).
Point C is at (1,1) and point D is at (3,5)

Answer 1

@ganeshie8 Please help me!

Answer 2

First of all we need to find the slope of given line and its equation.

Answer 3

So we use the slope formula?

Answer 4

To do this we use slope formula:
\[\frac{ y_1-y_2 }{ x_1-x_2 }=\frac{ 1-5 }{ 1-3 }=\frac{ -4 }{ -2 }=2\]

Answer 5

the slope of the given line is 2

Answer 6

slopes of perpendicular lines are negative reciprocals

Answer 7

what is a negative reciprocal to 2?

Answer 8

don't the prduct of their slopes always -1

Answer 9

they are

but to find the equation we need to find a negative reciprocal

Answer 10

-0.5

Answer 11

yeah but we will better write it as -1/2

Answer 12

Oh sorry.

Answer 13

so we have
y=mx+b
y=-1/2x+b
now substitute the point and solve:
6=-1/2*(-1)+b
6=1/2+b
b=?

Answer 14

Wait what do we substitute B with, its 2 right sorry im really stupid

Answer 15

look:
y=mx+b where m is slope:
m=-1/2

y=-1/2x+b
now we need to solve for y-intercept (b).

to do this we substitute the point:
6=-1/2*(-1)+b
b=?

Answer 16

OHHH I GET IT NOW THANK YOU!!!

Answer 17

yeah

so we solve for b and then get equation y=-1/2x+?

Answer 18

the answer is y=2x-13

Answer 19

nooooooooo

Answer 20

why you changed -1/2 to 2?

Answer 21

Oh because don't we bring it over to the other side so it changes to 2

Answer 22

noonon
we found a slope of given line: 2

then we found slope of line perp to it: -1/2

thus we have y=-1/2+b
6=-1/2*(-1)+b
b=6-0.5=5.5

we get y=-1/2x+5.5

Answer 23

OHHHHH I feel stupid lol THANKS!!!