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: 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 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 |
Begin
(prepare) |
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). |
|
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 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.
|
|
Engage | Next 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) #28─36 and Page 310, (on graph paper) #37─48
|
|
Assess (formative) | Click HERE to download the Graded Assignment. |
|
|
|