Lesson 2-3: Use Graphs to Determine Proportionality

Property

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

Examples

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 $(0, 0)$.

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

Property

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

Property

To solve problems using a graph of a proportional relationship:

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

Examples