Linear Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written 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 equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

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

Back

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

Front

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

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation.

Front

If Bob saves $40 per month starting with $150, what is the equation for his savings after x months?

Back

y = 40x + 150

Front

A music app charges $2 plus $1.29 per song. Write the equation for downloading x songs.

Back

y = 1.29x + 2

Front

What is the equation for Juanita's cell phone bill if she pays $15 per month plus $0.20 per minute?

Back

C = 15 + 0.20x

Front

In the dance club example, what is the fixed cost (startup fee)?

Back

$30

Front

What is the equation for the total cost of a holiday meal for x people at $12.50 each plus a $30 delivery fee?

Back

y = 12.5x + 30

Front

How do you identify the fixed cost in a linear equation from a word problem?

Back

The fixed cost is the amount that does not change with the number of items or services used, often represented by the y-intercept.