Identifying Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a graph to be non-linear?

Back

A non-linear graph does not form a straight line. It can curve or have varying slopes, indicating that the relationship between the variables is not constant.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the definition of a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, represented by the value of y when x = 0.

Front

Can a linear function be non-proportional?

Back

Yes, a linear function can be non-proportional if it has a y-intercept other than zero. For example, y = 2x + 3 is linear but not proportional.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 1/2x + 9.

Front

What is an example of a non-linear function?

Back

An example of a non-linear function is y = x^2 or y = 15/x.

Front

What does it mean for a function to be proportional?

Back

A proportional function is a linear function that passes through the origin (0,0), meaning it can be expressed in the form y = kx, where k is a constant.