# Ratios and Proportions / Connecting Ratios to Equations

Activity 10 of 15
Students generate slope triangles from the graph of a collection of equivalent ratios, thus leading to the notion of a proportional relationship. They use parallel grids to compare the tables, graphs, and equations for different unit rates.

## Planning and Resources

Objectives
Students should understand and identify the constant of proportionality, k, as the unit rate or the slope of a line through the origin. They can connect ratios to equations of a line through the origin: a:b → y= $\frac{b}{a}$ x

Vocabulary
proportional relationship
constant of proportionality
slope triangle

Standard:

## Lesson Snapshot

#### Understanding

A proportional relationship is formally associated with an equation, and the slope of the line representing the proportional relationship is associated with the notion of unit rate.

### What to look for

This lesson focuses on the fact that a proportional relationship can be described by an equation of the form y = kx, where k is a positive constant, often called a constant of proportionality. The rate of change in y for a given unit in x will be constant for the points on the line.

### Sample Assessment

Order the equations below in terms of steepest slope to least steep.
a. y = $\frac{2}{3}$ x
b. y = 2x
c. y = $\frac{1}{3}$ x
d. y = x