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

If they satisfy a linear relationship

means if they lie on the same line

you have 3 points. You only need 2 of them to find the equation of a line through them

Answer 2

you could try to find the equation

y = m x + b

where m is the slope, and b is the y-intercept

or you could use the formula

y - y0 = m( x - x0)

where (x0,y0) is a point on the line, and m is the slope.

Answer 3

a thought i have is to move this to the origin: zero out one of the points and move the rest by the same amount

{ (8, -1), (20, -10), (-12, 14) } ( x , 60)
-8 +1 -8 +1 -8 +1 -8 +1
----------------------------- -------
0 0 12 -9 -20 15 x-8, 61
-9/12 -15/20 61/(x-8) they should all be equal
-3/4 -3/4 proportions

\[\frac{-3}{4}=\frac{61}{x-8}\]

but tis is just one way to look at it

Answer 4

wait so are you saying that the x value would have to be -3/4??