Linear Function Applications

Front

Define a linear function.

Back

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

Front

What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What does the y-intercept represent in a linear function?

Back

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

Front

In the equation y = 2x + 3, what is the slope?

Back

The slope is 2.

Front

In the equation y = 2x + 3, what is the y-intercept?

Back

The y-intercept is 3.

Front

What is an independent variable?

Back

An independent variable is a variable that represents the input or cause in a function. It is usually denoted as x.

Front

What is a dependent variable?

Back

A dependent variable is a variable that represents the output or effect in a function. It is usually denoted as y.

Front

How do you identify the dependent and independent variables in a real-world scenario?

Back

The independent variable is the one that you can control or change, while the dependent variable is what you measure or observe as a result.

Front

What is the equation for a linear function that describes a cost of $5 per item with a fixed fee of $10?

Back

y = 5x + 10.

Front

If a function is represented as y = 4x - 2, what happens to y when x increases by 1?

Back

When x increases by 1, y increases by 4.