# Write an equation of the line shown in the graph of this equation

## How to find the equation of a line on a graph

We'll try it with the point 2, 3. So the line is going to look like this. A horizontal line indicates a constant output, or y-value. Using these two points, we can calculate the slope of this line. If you go back one, two, three, four, five-- you move up 1. No matter how much we change our x, y does not change. The way you verify that is you substitute x is equal to 0. Or it's equal to m plus b. If you go back that's negative 5. If you go backwards, if you move 5 backwards-- instead of this, if you view this as 1 over negative 5. Then you move up 1. I think it's pretty easy to verify that b is a y-intercept. Let me write that.

We'll try it with the point 2, 3. It doesn't really matter whether you subtract the values of point A from the values of point B, or the values of point B from the values of point A.

Our change in y is positive 3. It's always easier to think in fractions.

Now it makes sense. You can't subtract the y value of point A from the y value of point B, and the x value of point B from the x value of point A - your answer will be wrong.

We know the point 0, b is on the line.

## Graph to equation

You remember we're saying y is equal to mx plus b. You can't exactly see it there, but you definitely see it when you go over by 3. Here is b is 0. We'll try it with the point 2, 3. That's our y-intercept, right there at the origin. That's our starting point. Or the inclination of the line. One, two, three. So we also know that the point 1, m plus b is also on the line.

So b is equal to 1.

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