This is a remix of "Comparing Speeds in Graphs and Equations" by Illustrative Mathematics. The activity can be used to introduce the characteristics of direct variations. There is also a link to a direct and inverse variation foldable.

Determining direct variationMathematics Instructional Plans (MIPs) help teachers align instruction with the 2016 Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

This a foldable that can be used for teaching the characteristics of direct and inverse variation.

In Module 1, students build upon their Grade 6 reasoning about ratios, rates, and unit rates to formally define proportional relationships and the constant of proportionality. In Topic A, students examine situations carefully to determine if they are describing a proportional relationship. Their analysis is applied to relationships given in tables, graphs, and verbal descriptions.
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In Grade 6, students interpreted expressions and equations as they reasoned about one-variable equations. This module consolidates and expands upon student's understanding of equivalent expressions as they apply the properties of operations (associative, commutative, and distributive) to write expressions in both standard form (by expanding products into sums) and in factored form (by expanding sums into products). They use linear equations to solve unknown angle problems and other problems presented within context to understand that solving algebraic equations is all about the numbers. It is assumed that a number already exists to satisfy the equation and context; we just need to discover it. A number sentence is an equation that is said to be true if both numerical expressions evaluate to the same number; it is said to be false otherwise. Students use the number line to understand the properties of inequality and recognize when to preserve the inequality and when to reverse the inequality when solving problems leading to inequalities. They interpret solutions within the context of problems. Students extend their sixth-grade study of geometric figures and the relationships between them as they apply their work with expressions and equations to solve problems involving area of a circle and composite area in the plane, as well as volume and surface area of right prisms.
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In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module. Also, students learn to apply the skills they acquired in Grades 6 and 7 with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.
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Determining inverse variationMathematics Instructional Plans (MIPs) help teachers align instruction with the Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.