Question

Write the equation of the line that passes through the point (1,3) and is perpendicular to the line y = 1/2x - 1

Answer 1

can you tell me the slope of this line ?
y = 1/2x - 1 ??

Answer 2

In y = mx + b form, the slope is in the m position...so the slope of this line is 1/2. Do you understand that ??

Answer 3

yes

Answer 4

but we are looking for a perpendicular slope....and perpendicular slopes have negative reciprocal slopes. All that means is we are going to have to " flip " the slope and change the sign. That is the negative reciprocal.
So lets flip the slope and change the sign....1/2....neg reciprocal is -2/1 or just -2.
So our perpendicular line needs to have a slope of -2. Do you understand so far ??

Answer 5

Yes. With the slope being -2 do you go to find the y-intercept next?

Answer 6

yes...
use y = mx + b
slope(m) = -2
(1,3)...x = 1 and y = 3
now we basically sub in our info and solve for b....can you do that ?

Answer 7

In y = mx + b, the b stands for your y intercept

Answer 8

where did you get the (1,3)?

Answer 9

those are your points given in your original question.

Answer 10

do you need help in setting up the equation ?

Answer 11

Ok & Yes.

Answer 12

y = mx + b
slope(m) = -2
(1,3)...x = 1 and y = 3
now we sub and find b, the y intercept

3 = -2(1) + b
3 = -2 + b
3 + 2 = b
5 = b

have I lost you yet ??

Answer 13

No, i understand what you did there.

Answer 14

so we know out slope (m) is -2 and our y intercept (b) is 5...
so your perpendicular line passing through (1,3) is : y = -2x + 5

Answer 15

if you have any questions please ask them now :)

Answer 16

Thank you so much! I actually understand how to do it now? Is it the same working out process with parallel?

Answer 17

not quite....parallel lines will have the same slope. So if you were looking for a parallel line .....your slope would be the same as in the original line....your parallel slope would be 1/2....but for perpendicular, you need negative reciprocal slopes...thats when you flip the slope and change the signs.

Answer 18

Ok now i get you. You keep the same but still do the sub in stuff to still find b..right?

Answer 19

yep ^^...thats right :)

Answer 20

Ok. Thank You! (:

Answer 21

no problem :)