Linear Function Applications

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 the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

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

Back

The y-intercept (b) is the value of y when x is 0. It represents the starting point of the function on the y-axis.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the fixed costs and variable costs, and express the relationship in the form y = mx + b.

Front

In the equation y = 48x + 140, what do the numbers 48 and 140 represent?

Back

In this equation, 48 represents the hourly labor cost (slope), and 140 represents the fixed cost for parts (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

How do you find the height of an elevator after a certain time using the equation y = -3.8x + 290?

Back

Substitute the time (x) into the equation to calculate the height (y). For example, for x = 14 seconds, y = -3.8(14) + 290.

Front

Write the linear function for a car rental company that charges $56 plus $0.30 per mile driven.

Back

The linear function is y = 0.30x + 56, where x is the number of miles driven.

Front

What is the total cost equation for renting a paddle boat for h hours if the rental fee is $15 plus $2 per hour?

Back

The total cost equation is C = 2h + 15.