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 one-unit increase 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 situation with a fixed cost and a variable cost?

Back

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

Front

If a cell phone plan costs $15 per month plus $0.20 per minute, how would you express the total cost for x minutes?

Back

C = 15 + 0.20x.

Front

What is the equation for a fitness club membership that starts with 80 members and increases by 15 each month?

Back

y = 15x + 80, where x is the number of months.

Front

How do you represent a situation where something is decreasing over time?

Back

You can represent it with a negative slope in the equation, such as y = initial value - rate of decrease * time.

Front

What is the equation for a man descending from 100 feet at 30 feet per minute?

Back

y = -30x + 100.

Front

How do you calculate the total cost of renting a paddle boat with a deposit and hourly fee?

Back

C = deposit + (hourly fee * hours rented). For example, C = 15 + 2h.

Front

What does it mean for a relationship to be linear?

Back

A linear relationship means that there is a constant rate of change between the two variables, resulting in a straight line when graphed.