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 independent variable in a linear function?

Back

The independent variable is the variable that represents the input of the function, often denoted as x.

Front

What is the dependent variable in a linear function?

Back

The dependent variable is the variable that represents the output of the function, often denoted as y.

Front

In the equation y = mx + b, what does 'm' represent?

Back

In the equation y = mx + b, 'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Front

In the equation y = mx + b, what does 'b' represent?

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

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

Back

The independent variable is what you change or control, while the dependent variable is what you measure or observe.

Front

Write an equation for a situation where a taxi charges a flat fee of $3 plus $2 per mile driven.

Back

y = 2x + 3, where y is the total cost and x is the number of miles driven.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

Front

In a graph, which axis typically represents the independent variable?

Back

The x-axis typically represents the independent variable.

Front

In a graph, which axis typically represents the dependent variable?

Back

The y-axis typically represents the dependent variable.