| Slope-Intercept Form (y = mX + b) |
| GOAL: I can solve write linear equations is Slope-Intercept form given an unformatted equation. |
| Text reference: Chapter 5, section 3B, pages: 306 ─ 312 |
Illinois learning standard: 8.A.3b |
NCTM standard: XX─XX |
| Lesson Vocabulary |
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| 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. |
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Strategies and Content Practice |
Notes |
Begin
(prepare) |
Check for prior knowledge.
Review the variable and constant movement techniques.
See Chapter 2, Sections 2 for a refresher and videos. |
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| Engage | Students need to be able to rearrange the term of a linear equation to get the equation into slope-intercept form ( y = mx + b ).
In order to do this, they need to be able to apply the movement techniques they learned in chapter 2, section 2.
To engage the students, have the try the Sample Problem below.
After they have tried a few (or all) click on the Solutions link to see a step-by-step explanation of how to get the equation into slope-intercept form.
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Assess
(formative) |
After example problems and videos, have students try to solve the Sample Problems below. After students have had time to complete them, click on the Solutions link and go through the step-by-step process for solving each problem. Repeat if necessary with additional example problems in the book and re-assess. |
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| Apply |
Practice Assignment (coming soon)
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Assess
(formative) | Answers to the Practice Assignment (coming soon)
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| | Apply | Click HERE to download the Graded Assignment. | |
| Sample Problems |
Sample Solutions |
| 2y + 4x = 8 |
Click Here for step-by-step solution. |
| 4y ─ 3 = 8x |
Click Here for step-by-step solution. |
| 3y = 9x |
Click Here for step-by-step solution. |
| 3y + 2x = 12 ─ 4x |
Click Here for step-by-step solution. |
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