Linear Functions Word Problems

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 of a linear function represent?

Back

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

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you write an equation for a linear function from a word problem?

Back

Identify the quantities involved, determine the rate of change (slope), and the starting value (y-intercept), then use the form y = mx + b.

Front

If a family drinks 5 bottles of water per day from a case of 48 bottles, how do you express the number of bottles left after x days?

Back

y = 48 - 5x.

Front

Bob saves $40 per month starting with $150. Write the equation for his savings after x months.

Back

y = 40x + 150.

Front

What type of graph does a linear function produce?

Back

A linear function produces a straight line on a graph.

Front

What is the cost equation for snowboarding if it costs $15 per hour plus a $25 rental fee?

Back

y = 15x + 25.

Front

In the equation y = 1.5x + 20, what does 1.5 represent?

Back

1.5 represents the cost per ride at the amusement park.

Front

How do you determine if a function is linear?

Back

A function is linear if it can be represented by a straight line and has a constant rate of change.