This is a 3 day mini-unit I did with my 9th grade Algebra 1 students to teach writing equations in Slope-Intercept form using Point Slope form.
Point slope form is the easiest, most effective way to help students write linear equations in slope-intercept form. On day 1, we review how to write equations in slope-intercepts form given a the slope and the y-intercept. I then introduce point slope form, and have students learn/practice writing equations with a slope and point that is not the y-intercept. Students start by writing the point and slope into the point-slope form, and then convert it to slope intercept.
On day 2, we practice writing equations in slope-intercept form given a graph that contains a point on the y-axis, and then move into writing an equation in point slope form when the line does not contain the y-intercept (or the y-intercept is not a whole number). Next, we move into writing equations given any two points on the line.
On day 3, we practice writing equations in slope-intercept form given points on a table. This is similar to what they did on day 2 (where they were given two points on the line), but for some reason when the points are offered in table format students have more difficulty. I always tell students to use the first two points on the table, and solve it like they did on day 2.
Most of my students were proficient at this skill (writing equations in slope-intercept form of a linear equation given a graph, a table, or two points on the line) by the end of day 3.
I have included answer keys for all 3 days. Depended on the length of your class periods, this may be squeezed into a 2 day unit or stretched into 4 days.