1) The Slope Formula: m = (y2 - y1)/(x2 - x1)
2) Vertex Formula: y = m(x - h) + k
3) Slope-Intercept: y = mx + b
And I finally showed them point-slope form
4) Point-Slope: y - y1 = m (x - x1)
We discuss what is similar and different about each of the formulas. I show them how to convert the slope formula to point-slope, then point-slope to vertex, and if we substitute h with 0 in vertex form we get slope-intercept. It was beautiful!!
Next, we discussed the two methods the students used yesterday to write the equation of the line that passes through the points (6, 7) and (10, 9). The two methods they came up with are graphing or using the vertex formula.
Then I showed them how they could use the slope formula, or slope-intercept, or even our new one Point-Slope.
This is what my boards looked like at the end of class. The formulas on the right board and our work on posters on the left board.