Learn on PengiReveal Math, AcceleratedUnit 2: Proportional Relationships

Lesson 2-3: Use Graphs to Determine Proportionality

In this Grade 7 Reveal Math Accelerated lesson from Unit 2, students learn how to use coordinate plane graphs to determine whether a relationship is proportional by identifying whether the line passes through the origin and has a constant ratio of y to x. Students practice finding the constant of proportionality from a graph by locating the point where x equals 1, applying these skills to real-world contexts like SONAR depth measurement and bike share pricing. The lesson builds on proportional relationship concepts to help students distinguish proportional from non-proportional linear relationships visually.

Section 1

Graphing Proportional Relationships

Property

If quantities yy and xx are in proportion then the graph of pairs (x,y)(x, y) in this relation will be a straight line through the origin. That line is characterized by the assertion that yx\frac{y}{x} is constant, and in fact, is the constant of proportionality.

Examples

Section 2

Identifying Non-Proportional Relationships from Graphs

Property

A relationship represented by a graph is non-proportional if it fails one or both of the following conditions:

  1. The graph is not a straight line.
  2. The graph does not pass through the origin (0,0)(0, 0).

If a linear graph has an equation of the form y=mx+by = mx + b where b≠0b \neq 0, it represents a non-proportional relationship.

Section 3

Calculating the Constant of Proportionality from a Graph

Property

The constant of proportionality can be found from the graph of a proportional relationship by identifying any point (x,y)(x, y) on the line (other than the origin) and calculating the ratio of the yy-coordinate to the xx-coordinate:

r=yxr = \frac{y}{x}

Section 4

Solving Proportional Problems Using Graphs

Property

To solve problems using a graph of a proportional relationship:

  1. Identify a clear point (x,y)(x, y) on the line to find the constant of proportionality, k=yxk = \frac{y}{x}.
  2. Use the constant kk to find unknown values using the equation y=kxy = kx.
  3. Alternatively, locate a given xx-value or yy-value on the axis and trace to the line to read the corresponding unknown value directly.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Graphing Proportional Relationships

Property

If quantities yy and xx are in proportion then the graph of pairs (x,y)(x, y) in this relation will be a straight line through the origin. That line is characterized by the assertion that yx\frac{y}{x} is constant, and in fact, is the constant of proportionality.

Examples

Section 2

Identifying Non-Proportional Relationships from Graphs

Property

A relationship represented by a graph is non-proportional if it fails one or both of the following conditions:

  1. The graph is not a straight line.
  2. The graph does not pass through the origin (0,0)(0, 0).

If a linear graph has an equation of the form y=mx+by = mx + b where b≠0b \neq 0, it represents a non-proportional relationship.

Section 3

Calculating the Constant of Proportionality from a Graph

Property

The constant of proportionality can be found from the graph of a proportional relationship by identifying any point (x,y)(x, y) on the line (other than the origin) and calculating the ratio of the yy-coordinate to the xx-coordinate:

r=yxr = \frac{y}{x}

Section 4

Solving Proportional Problems Using Graphs

Property

To solve problems using a graph of a proportional relationship:

  1. Identify a clear point (x,y)(x, y) on the line to find the constant of proportionality, k=yxk = \frac{y}{x}.
  2. Use the constant kk to find unknown values using the equation y=kxy = kx.
  3. Alternatively, locate a given xx-value or yy-value on the axis and trace to the line to read the corresponding unknown value directly.

Examples