We want to match each vocabulary term with its definition. Let's take a look at each definition, one at a time.

Definition $1$

Consider the given definition.

A function whose graph is not a straight line

This definition is about a function that is not a straight line. When a function cannot be represented using a straight line it is said to be a nonlinear function.

Definition $2$

Let's take a look at the next definition.

The slope of a line

Remember that the slope of a line can be found as the ratio of its

rise

to its

run .

m = \frac{rise}{run}

The rise and the run of a line can be found as the change in

y -

values and the change in

x -

values, respectively.

This is the same as finding the rate of change of the function. Since it is a straight line, it is a linear function and has a constant rate of change.

Definition $3$

Consider the following definition.

A relation in which each input, or $x -$ value, has exactly one output, or $y -$ value

We are talking about a special type of relation where each input has exactly one output assigned. There are no further specifications to the relation and it satisfies the definition of function.

Function
A function is a relation in which each input is assigned to exactly one output.

Definition $4$

Let's read the next definition.

The value of the output when the input is $0,$ or the $y -$ intercept of the graph of a line

Since we are talking about a line, we will take a look at a linear equation that describes a linear function.

y = m x + b

Let's also take a look at the graph!

The $y -$ intercept is the value at which the input is $0 .$ This is how the graph starts before there is any change to the input, so this is also known as its initial value.

Definition $5$

Consider the last given definition.

A period of time between two points of time or events

Time is usually used as the independent variable in most cases, so it is placed on the $x -$ axis. A period of time can be seen in a graph as a $horizontal$ $distance .$ We use this distance to describe the behavior of the $y - values .$

This space between two $x -$ values is known as an interval. This is also the only remaining choice of the vocabulary terms!

Summary

Finally, let's summarize our findings by making a table with the definitions and their matching vocabulary terms.

Definition	Vocabulary Term
A function whose graph is not a straight line	nonlinear function
The slope of a line	constant rate of change
A relation in which each input, or $x -$ value, has exactly one output, or $y -$ value	function
The value of the output when the input is $0,$ or the $y -$ intercept of the graph of a line	initial value
A period of time between two points of time or events	interval

Definition 1

Definition 2

Definition 3

Exercise