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.
