Where does point-slope form come from?

Unit 3 covered Linear Equations and Inequalities. During this unit students learned different ways to write linear equations: slope-intercept form, point-slope form, and standard form. My showcase lesson is about the day I introduced point-slope form to the students.

This lesson used students' prior knowledge of the slope formula and their strategies for solving literal equations to derive the point-slope formula. (Slope formulas seen in Figure 1)

Students started with their basic formula for slope and they were asked to solve for change in y. They then used their knowledge of change in y and change in x to substitute those formulas into their literal equation. (Steps seen in Figure 2)

Figure 2

Figure 1

Once students reached the final literal equation, I asked them if they would know what to do if I gave them a set of points and slope. Students were quick to say yes, but were more challenged than they thought when they saw the ordered pairs given to them. After students were prompted to label their ordered pairs as they have done in the past (x1, y1, x2, y2) they were able to plug everything in as they originally thought. (The given information and final equation is seen in Figure 3)

Figure 3

Students were then informed that they just wrote the linear equation of a line with a slope of 4 that went through the point (2,1). We discussed the need of an x and y in our equation so that it is solvable and that every time they write in point slope form, their x2 and y2 will be their basic x and y that they need. Students thought it was super cool that they took something they already knew and were able to create the new form they needed for the current unit. Following this exploration, students completed notes for their journals over writing and graphing using point-slope form given combinations of points, slopes, or y-intercepts.

Menu Choice Board Day!

During Unit 2, Slope and Linear Functions, their needed to be a day filled with mixed practice before we continued on in the unit. To do so, I created a menu choice board for the students. The menu board allowed students to complete activities on their own or with partners, on a laptop or on a physical piece of paper, or with basic practice or summarizations of concepts. The menu board can be seen by clicking the button below.

This form of review also allowed for me to make sure that all students felt their was an activity that they felt they could achieve. The students who enjoy tangible things could complete a card sort, students who enjoy creating things could create visuals to summarize concepts, and students who just like to work on their own could complete practice problems. This also allowed for the teacher to differentiate the lesson by informing certain students to complete certain activities in content areas that they were struggling in. While few students were able to complete more than three activities, students loved this activity. During my student survey, many students expressed that they would like to have another menu board day.