Question

How do you find the equation of a line that passes through the point (-1,-3) and is perpendicular to the line with the equation y=3/4x+11/4

Answer 1

first of all, a perpendicular line will have a negative reciprocal slope.
can you tell me the slope of y = 3/4x + 11/4 ?? Do you know how ?

Answer 2

one second,

Answer 3

remember that in y = mx + b form, the number in the m position is the slope. So what number is in the m position in y = (3/4)x + 11/4 ?

Answer 4

3/4

Answer 5

correct...now that is the slope of the original equation...we now need the negative reciprocal of that. All that means is " flip " the slope and change the sign. For example, if the slope was 1/2, the negative reciprocal would be -2/1...see how I flipped the slope and changed the sign. So now what is the negative reciprocal of 3/4 ?

Answer 6

-4/3

Answer 7

correct..
Now we will use y = mx + b
slope(m) = -4/3
(-1,-3)...x = -1 and y = -3
and since we know slope(m) and our x and y points, we need to find b, the y intercept
now we sub
y = mx + b
-3 = -4/3(-1) + b
-3 = 4/3 + b
-3 - 4/3 = b -- find common denominator
-9/3 - 4/3 = b
-13/3 = b

so your perpendicular equation is : y = -4/3x - 13/3
any questions at all ?

Answer 8

not anything specific, im still kind of confused by this. would you mind helping me work through a few more problems like this?

Answer 9

I do not mind....what else you got ?

Answer 10

point (1,3) that is perpendicular to the line y=2x-8

Answer 11

first we find slope of original equation,,,can you tell me the slope of the original equation ?

Answer 12

2, so would you write that as 2/1?

Answer 13

you can just write it as 2.....or if you want to, you can use 2/1....and we want a perpendicular line...so we need negative reciprocal of 2/1...do you know that ? Remember that negative reciprocal is when you flip the slope and change the sign. So what is the new slope we need ?

Answer 14

-1/2

Answer 15

correct....see...your getting this
Now we use y = mx + b
slope(m) = -1/2
(1,3)...x = 1 and y = 3
now we sub and solve for b
y = mx + b
3 = -1/2(1) + b
3 = -1/2 + b
3 + 1/2 = b -- find common denominator
6/2 + 1/2 = b
7/2 = b

so our perpendicular equation is : y = -1/2x + 7/2

Answer 16

I am so sorry....I kinda lost track of time...I have to go now but I will be back on later...sooo sorry

Answer 17

it's okay, thank you so much @texaschic101 !

Answer 18

your very welcome :)