Graphs of Proportional Relationships

Recall that a proportional relationship can be represented by an equation of the form *y* = k*x*, where k is a constant.

The constant, k, is the constant of proportionality, or unit rate.

Notice in the equation *y* = k*x*, if *x* equals 1, then *y* equals k.

So, on the graph of a proportional relationship, when *x* equals 1, the corresponding *y*-value is the constant of proportionality.

Also, in the equation *y* = k*x*, notice if *x* equals 0, then *y* also equals 0.

So, on a coordinate grid, a line drawn through points which represent a proportional relationship, and extended through the *x*-axis, contains the point (0, 0).

**Does the graph represent a proportional relationship?**

The points on the graph lie on a straight line, and the graph contains the point (0, 0). So, the graph does represent a proportional relationship.

**Identify the constant of proportionality, and interpret the unit rate.**

When *x* equals 1, the corresponding *y*-value is the constant of proportionality.

When *x* equals 1, *y* equals 10.

The constant of proportionality is 10.

The unit rate can be interpreted as $10 per ticket, or 1 ticket costs $10.

**Interpret the point (0, 0).**

The point (0, 0) corresponds to an *x*-value of 0, and a *y*-value of 0.

*x*-values represent the number of tickets, and *y*-values represent the cost.

So, the point (0, 0) can be interpreted as zero fair tickets cost $0.