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?
We know the slope is 1/7 and we can estimate the y-intercept, but how can we 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.