**Step 1:**Find slope

**Step 2:**Write in point slope form

**Step 3:**Solve for y to get slope-intercept form

**Step 4:**Rewrite in Standard Form

I've usually encouraged this process as it seemed to be the efficient way to

*cover*the majority of these skills. But this year, I kept it much more loose. We all agreed that if the two points given define a line with an integer for the y-intercept, then it's pretty easy to write in slope intercept form.

I mean, c'mon, we've got the slope and we

*see*the y-intercept plain as day.

But what happens here?

*know*the y-intercept?

**Rate of Change**

Most of the time when we discuss Slope we talk about the path from one lattice point to another. For example, the slope between A and B is 1/7 because we go up 1 and over 7 to get from A to B.

But we have been doing more with rate of change as a unit rate which means that for every 1 unit of horizontal change, we increase 1/7. Yeah, I know that sounds elementary, but it makes a difference in how your kids see these things.

If each step increases 1/7, we increase a total of 4/7 to get to the y axis. Therefore, y-intercept is 4 4/7. We still talk about point-slope form, but this beats the heck out of the plug and chug that usually goes along with it.

## 3 comments:

This is good for your visual types.

I'm of the mind that there are multiple intelligences in math: visual, numerical, and analytical.

Some people like to see the pictures like this and understand better that way. Others like to make t-charts and see how the numbers make patterns and play out. Others still understand the symbolic manipulation best.

I guess I'm just saying not to discount the previous ways you were doing it.

I'm not trying to pit one against the other. I just think that the visual gives context to the symbolic manipulation. We are really focusing on multiple representations this year and I think that this helped. A lot.

This seems useful. Overall, graphing lines is too often done too algorithmically. Let kids figure it out for themselves, given a variety of concepts and connections like the ones you mention here.

What about lines where you can't see them cross any lattice points? Lines with irrational slopes - Can you graph such a line? Including questions such as this one really clarifies the whole topic.

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