Linear Functions: Tables, Graphs, and Equations

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has a constant rate of change and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not create a straight line when graphed. Its rate of change is not constant, and it can be represented by curves or other shapes.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This means that no x-value is repeated with different y-values.

Front

How can you tell if a table represents a linear function?

Back

A table represents a linear function if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is calculated as the change in y divided by the change in x (rise over run).

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

What does a graph of a linear function look like?

Back

A graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

Front

What does a graph of a non-linear function look like?

Back

A graph of a non-linear function can take various shapes, such as curves, parabolas, or circles, and does not form a straight line.

Front

How can you determine if a graph is a function?

Back

You can use the vertical line test: if a vertical line crosses the graph at more than one point, then it is not a function.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3, which represents a straight line with a slope of 2 and a y-intercept of 3.