Question

How can you write the equation for a linear function if you know only two ordered pairs for the function?

Answer 1

1. m
2. One set of ordered pairs
3. b

To show why this is, I’m going to explain how to write the equation for a linear function with two random sets of ordered pairs - (1,0) and (5, 8).

First, find the slope. The formula for slope is m = (y2 - y1)/(x2-x1) where m is the slope and (x1, y1) and (x2, y2) are two sets of points.

This is why #1 is m. M is the letter used when finding slope.

To find m, I plug in the two sets of ordered pairs.

m = (8-0)/(5-1)
m = 8/4
m = 2

An equation for a line (linear function) is written in something called slope-intercept form. It looks like y = mx + b. m is the slope and b is the y-intercept (number y equals when x = 0). If m = 3 and b = 1, the equation would be y = 3x + 1.

Here, you have just solved for m and know it equals 2. Plug that value in for m.

y = 2x + b

To solve for b, plug one ordered pair in for x and y. I will use (1,0)

0 = 2(1) + b
0 = 2 + b
-2 = b

Now that you know b = -2, plug that in for b.
y = 2x - 2. Now you have the equation fo the line.