4.4 Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 value of y when x is 0. It represents the point where the line crosses the y-axis.

Front

Write the equation for a linear function that represents a waitress's salary based on hours worked and tips earned.

Back

S = 3h + 0.90d, where S is the salary, h is hours worked, and d is dollars in tips.

Front

What is the equation for a plumber's charge based on house call and hourly labor?

Back

y = 50 + 12x, where y is the total charge, 50 is the house call fee, and 12 is the hourly labor charge.

Front

How can you determine if a function is 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

What is the equation for Juanita's cell phone bill based on airtime usage?

Back

C = 0.20x + 15, where C is the monthly bill and x is the number of minutes used.

Front

What does it mean for a graph to be linear?

Back

A linear graph is a graph that forms a straight line, indicating a constant relationship between the variables.

Front

Identify the components of the equation S = 3h + 0.90d.

Back

In this equation, S is the total salary, 3h represents the hourly wage multiplied by hours worked, and 0.90d represents 90% of the tips earned.

Front

What is the significance of the constant term in a linear equation?

Back

The constant term (b) in a linear equation indicates the starting value of the dependent variable when the independent variable is zero.