Question from class: How do I make an equation from a line?

Way back in October we wrote equations in slope-intercept form or equations that look like y=mx+b where m and b are numbers. The number we put in place of m was the slope and b was the y-intercept.

So if we had this line:

We find the equation by finding the y-intercept or where the line crosses the y-axis and the slope. My line crosses at (0,3). Remember that the x value for the y-intercept will always be zero so we usually just say that the y-intercept is 3. So b=3

Then we find the slope. You have two options here, both start with choosing 2 points that are easy to find the coordinates of, meaning that the line crosses a point where the grid lines also cross. I chose (-1,0) and (2,9) because I liked them. There's no magic to the points I picked, any two would work.

Method 1: Pictures
In this method I am going to draw my rise and run between my points. The rise is blue, the run is 3. I count them out and set up my ratio of rise to run.

Method 2: Formula

Either way our slope is 3 so m=3. The equation is y=3x+3

I need it in different words or a few more examples.

Purple Math
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