Linear Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that represents 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 in a linear equation represent?

Back

The slope 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 is the y-intercept in a linear equation?

Back

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

Front

How do you write an equation for a total cost that includes a fixed fee and a variable fee?

Back

The equation can be written as C = fixed fee + (variable fee per unit * number of units).

Front

If a cell phone plan charges a monthly fee plus a per-minute fee, how would you express the total cost?

Back

Total cost (C) can be expressed as C = monthly fee + (per-minute fee * number of minutes used).

Front

How do you find the break-even point in a cost comparison problem?

Back

Set the cost equations of both options equal to each other and solve for the variable (e.g., hours, minutes).

Front

What is the formula for calculating total cost in a rental situation?

Back

Total cost (C) = rental fee + (hourly rate * number of hours rented).

Front

How do you determine the total cost for a group meal including delivery?

Back

Total cost (y) = cost per person * number of people + delivery fee.

Front

What is the significance of the startup fee in a membership model?

Back

The startup fee is a one-time cost that must be paid before any recurring fees (like monthly fees) begin.

Front

How can you express a situation where costs increase over time?

Back

Use a linear equation where the total cost is a function of time, such as C = initial cost + (rate of increase * time).