Math Mammoth Graphing Linear Equations

77 pages
(includes answers)

Sample pages (PDF)

Contents

Graphing Proportional Relationships 1

Slope, Part 3

Write the Slope-Intercept Equation

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Math Mammoth Graphing Linear Equations is a worktext that focuses on various aspects of graphing linear equations and on the concept of slope.

We start out by reviewing what it means when two variables are in a proportional relationship (direct variation, or proportional). Students learn that these relationships are always written in the form y = mx where m stands for the constant of proportionality, which is also the rate of change of the function, and in the context of graphing, the slope.

We spend one lesson comparing proportional relationships represented in different ways: given by a graph, a table of values, an equation, or a verbal statement.

Then, students learn about slope as the ratio of rise over run, or the change in y-values over the change in x-values. They find the slope of lines from a graph or from two points on the line.

The lesson “Slope, Part 2” presents a proof for the fact that it doesn't matter which two points on the line you use to calculate the slope. We also derive the equation y = mx for a line through the origin. In the following lesson, students learn to graph lines with a given slope, and also about vertical and horizontal lines.

Then it is time to derive the slope-intercept form of a linear equation: y = mx + b, and learn to use it in the context of graphing. Students also find that equation for already plotted lines.

Next, we take a closer look at horizontal and vertical lines and their equations. Then, the standard form is introduced. The last topic of the book is parallel and perpendicular lines. The book ends in a review lesson, followed by the answer key.

The book meets the Common Core Math Standards 8.EE.5 and 8.EE.6, plus provides material for related topics (e.g. vertical and horizontal lines, standard form, perpendicular and parallel lines).

The answers are appended.

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