Question

WHAT LINEAR FUNCTION EQUATION CAN BE REPRESENTED BY THE SET OF ORDERED PAIRS?

(-4,-6) (0,-3) (4,0) (12,6)

Answer 1

First find the slope by using the (y2-y1)/(x2-x1) equation with any given coordinates:
(6--3)/(12-0)=9/12=3/4 is the gradient
So far y=3/4x+b
The y intercept can be found when x=0 so use (0,-3) and the y intercept is -3
So the equation is y=3/4x-3
CHECK the equation works:
3/4 × 12=9, 9-3=6 so (12,6) works

Answer 2

Check out the slope of the line segment connecting (-4,-6) and (0,-3):
-3 - (-6) 3
m = ------------- = ----
0 - (-4) 4

Now use the point slope formula to derive the function:

y - 0 = (3/4)(x - 4) or y = (3/4)(x - 4 (answer)

check: Does (12,6) satify this formula?



Try again: Find the line connecting (4,0) and (12,6):
6 - 0 6 3
m = ---------- = ---- = ---- This is good news, since we got m = 3/4 earlier.
12-4 8 4

Try again to obtain the equation of this line with slope 3/4:

Use y = mx + b. Using the point (0, -3), -3 = (3/4)(0) + b. Then b = -3
and the line is y = (3/4)x - 3.

Check this using the point (-4,-6): Is the following true? -6 = (3/4)(-4) - 3
-6 = -3 - 3 TRUE

The desired linear function is y = (3/4)x - 3.