Question

Consider the set of ordered pairs {(8, -1), (20, -10), (-12, 14)}. If they satisfy a linear relationship, what is the value of x when y = 60?

Answer 1

First off the points do satisfy a linear relationship, and that can be verified by taking the slope for points 1 and 2 and then comparing that to slope for points 2 and 3.

To get the value of x, you can get the slope of (x, 60) and any of the other points and set that equal to the slope between any 2 of the 3 given points.

Answer 2

In case you are having trouble calculating slope, slope is "m" in the following:\[m = \frac{ y _{2} - y _{1} }{ x _{2} - x _{1} }\]for given points:\[(x _{1}, y _{1})\]and\[(x _{2}, y _{2})\]as long as the denominator is not "0".

Answer 3

okay ill try it out thanks

Answer 4

uw!

Answer 5

im not sure about this one. last time i did it i got -75 as x.

Answer 6

i dont think i got the right slope for (x, 60). how would you get that?

Answer 7

You are close but off by a little. Here's a graph that might help, and then I'll help you with the algebra in a follow-up post.

Answer 8

okay so is the slope -3/4?

Answer 9

Using points 1 and 2,

m = [-10 - (-1)] / (20 - 8) = -3/4

-3/4 = [60 - (-1)] / (x - 8)

Now you can solve for "x".

Answer 10

okay. thats my problem, i guess i just dont know how to solve for x. like how would i set that up?

Answer 11

Well . . .

I actually already set it up for you.

Answer 12

From my equation from 2 posts ago, just cross-multiplying:

24 - 3x = 244

Answer 13

ohh okay so -220/3?

Answer 14

well or -73.3

Answer 15

That's it! And you can look for that on the graph I attached above to see that "x" when y = 60.

Answer 16

okay thank you so much!!!!!

Answer 17

saved my life hah

Answer 18

uw! It's about -73 and 1/3 I'm now a lifeguard!

Answer 19

oh okay! haha

Answer 20

Good luck to you in all of your studies and thx for the recognition! @nechamoosh