Question

find an equation of the line that passes through (8,17) and is perpendicular to the line x+2y =2

Answer 1

the answer on my answer sheet is y=2x+1 and I dont know how they got it?

Answer 2

First solve for y

x+2y =2

2y =2-x

2y = -x + 2

y = (-x+2)/2

y = -1/2x + 1

So the slope of this given line is -1/2

Answer 3

Flip the fraction to get -2/1

then flip the sign to get +2/1 which is 2/1 = 2

So the slope of this perpendicular line is m = 2

Answer 4

Now use the point given (8,17) to find the y-intercept

y = mx+b

y = 2x + b ... plug in that perpendicular slope

17 = 2*8 + b ... plug in the given point

17 = 16 + b

17 - 16 = b

1 = b

b = 1

So we now know that m = 2 and b = 1 which explains why the answer is y = 2x + 1

Answer 5

why do you flip the sign from -2/1 to +2/1

Answer 6

Because when you have a given slope and you want to find the perpendicular slope you...

a) flip the fraction

AND

b) flip the sign

Answer 7

Another example

Given Slope: 1/3


Flip the fraction: 1/3 ----> 3/1

Flip the sign: 3/1 = +3/1 ----> -3/1 = -3


So the given slope is 1/3
The perpendicular slope is -3

Notice how if you multiplied 1/3 with -3, you will get -1

Answer 8

oh that makes a whole lot more sense thanks so much!

Answer 9

you're welcome