SlopeIntercept Form (y = mX + b) 
GOAL: I can write linear equations in SlopeIntercept form given two points and graph them. 
Text reference: Chapter 5, section 3A, pages: 306 ─ 312 
Illinois learning standard: 8.A.3b 
NCTM standard: XX─XX 
Lesson Vocabulary 

Linear Equation 
Is an equation that models a linear function. In other words, it is an equation that represents a straight line. 
Linear Equation Variable "X" (as in y = mX + b) 
The X variable in the SlopeIntercept linear equation ( y = mX + b ) CAN ONLY be raised to the first power, in other words, just X. The X variable CANNOT be raised to a higher power like X^{2}, X^{3}, or X^{4}. Also X CANNOT be used as an exponent like 2^{x}. Either of these two "NONOs" causes the line to turn into a curve (which we'll learn about later). 
"m" (as in y = mX + b) 
"m" stands for the Slope of the line. Slope is a measure of steepness of a line or something real like the steepness of a hill. Positive (+) slopes look like lines going UP as we look at them from left to right on a graph. Negative (─) slopes look like lines going DOWN as we look at them from left to right on a graph. Zero slopes look FLAT like horizontal lines when we look at them on a graph. Oh, and by the way, a straight UP and DOWN line (vertical) has an undefined slope because the slope is so steep it is infinite. 
"b" (as in y = mX + b) 
"b" stands for the YIntercept of the line. The YIntercept is the number value on the Yaxis (vertical axis) where the line crosses it. It could be positive or negative. 

Strategies and Content Practice 
Notes 
Begin
(prepare) 
Review the vocabulary terms and their extended definitions. Make sure students understand that the SlopeIntercept form of the linear equation contains an "X" and a "Y" BECAUSE, the line that it represents is drawn on a 2dimensional graph with an Xaxis and a Yaxis. Remind students of the XY Ttables they used in the past to come up with ordered pairs for plotting linear equations. HOOK students with the promise that in this section they will learn a much easier way to plot linear equations than their previous method of calculating ordered pair points. Call it the "Stepwise" method. 
I call the method of plotting linear equations using the YIntercept and Slope the "Stepwise" method. 
Engage 
Have students read pages 306  309. Read aloud same with students, emphasize definitions and example problems. Show demonstration videos for Lesson 53 (above). 

Assess
(formative) 
Demonstrate a few of the problems on page 310, # 7 ─ 27. Assess students' prior knowledge first three concepts: a) # 7 ─ 15, finding Slope and YIntercept from properly formatted SlopeIntercept equations. b) # 16 ─ 21, writing properly formatted SlopeIntercept equations give a Slope and YIntercept. c) # 22 ─ 27, writing properly formatted SlopeIntercept equations given a line graph. Demonstrate a few of each and then have students practice more of these in their notebooks until they understand these concepts.


Engage  Next you'll need to demonstrate the two new concepts for this lesson. The new concepts are: d) Writing a SlopeIntercept formed equation given two points that the line passes through Video Example using the points (─3, 6) and (4, ─8) Video Example using the points (─2, 4) and (4, 1) Video Example using the points (─3.5, 2.8) and (4.2, ─5.7) e) Graphing a line given a properly formatted SlopeIntercept equation. Video Example using y = 3/4x ─ 5 Video Example using y = ─2/3x + 8 Video Example using y = ─3x + 4 Video Example using y = ─4x
 
Apply 
Practice Assignment: Page 310, (in notebook) #28─36 and Page 310, (on graph paper) #37─48


Assess (formative)  Click HERE to download the Graded Assignment. 

