Slope-Intercept Form

We know how to use an equation to graph a line. But what if we want to write an equation for a line we already have?

An equation for a line is like a group of directions for graphing that line. Let's write some directions for graphing the line shown below:

When we're done with the directions, we can try to turn them into an equation.

In the picture shown above, Joan is at the origin. She can find a point on the line by crawling up the y-axis. The point where a line meets the y-axis is called the y-intercept, so we can tell Joan, "Find the y-intercept by crawling up the y-axis."

Joan follows our directions:

Now Joan needs to stick her tongue out along the line. She can do this by giving her tongue the same slope as the line. What is the slope of the green line?

m = (y₂ - y₁) / (x₂ - x₁)
= (4 - 3) / (4 - 2)
= 1/2

So we should tell Joan, "Give your tongue a slope of 1/2."

Joan leaves behind a red line identical to the green one.