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

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 Slope-Intercept 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 X2, X3, or X4.  
Also X CANNOT be used as an exponent like 2x.
Either of these two "NO-NOs" 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 Y-Intercept of the line.
The Y-Intercept is the number value on the Y-axis (vertical axis) where the line crosses it.
It could be positive or negative.

Strategies and Content Practice  Notes 
Review the vocabulary terms and their extended definitions.
Make sure students understand that the Slope-Intercept form of the linear equation contains an "X" and a "Y" BECAUSE, the line that it represents is drawn on a 2-dimensional graph with an X-axis and a Y-axis.
Remind students of the X-Y T-tables 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 "Step-wise" method.

I call the method of plotting linear equations using the Y-Intercept and Slope the "Step-wise" method.
Engage Have students read pages 306 - 309.
Read aloud same with students, emphasize definitions and example problems.
Show demonstration videos for Lesson 5-3 (above).
Demonstrate a few of the problems on page 310, # 7  27.
Assess students' prior knowledge first three concepts:
a) # 7  15, finding Slope and Y-Intercept from properly formatted Slope-Intercept equations.
b) # 16  21, writing properly formatted Slope-Intercept equations give a Slope and Y-Intercept.
c) # 22  27, writing properly formatted Slope-Intercept 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.

EngageNext you'll need to demonstrate the two new concepts for this lesson.
The new concepts are:
d) Writing a Slope-Intercept 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 Slope-Intercept 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) #2836 and
    Page 310, (on graph paper) #3748

Click HERE to download the Graded Assignment.