How can you write the equation for a linear function if you know only two ordered pairs for the function? Drag ties to complete the explanation. Tiles may be used once, more than once, or not at all.

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.