Real World Word Problems with Linear Equations

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 y with respect to x. It indicates how much y changes for a one-unit increase 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 is the point where the line crosses 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 it in the form y = mx + b.

Front

If a plumber charges a flat fee plus an hourly rate, how can you express the total cost as a linear equation?

Back

Total cost (y) = flat fee + (hourly rate * hours worked). For example, y = 50 + 25x.

Front

What is the total cost for 2.5 hours of labor if the hourly rate is $25 and there is a $50 service charge?

Back

Total cost = 50 + (25 * 2.5) = 50 + 62.5 = $112.50.

Front

How do you determine the total cost of x pounds of fruit if there is a fixed cost and a variable cost per pound?

Back

Total cost (y) = fixed cost + (cost per pound * x). For example, y = 2.50x + 3.

Front

What is the equation for the total cost of renting a canoe for x hours if there is a transportation fee and an hourly rental fee?

Back

Total cost (y) = transportation fee + (hourly rental fee * hours rented). For example, y = 30x + 20.

Front

How do you calculate the total cost at an amusement park if the cost is based on the number of rides?

Back

Use the equation y = 1.5x + 20, where x is the number of rides and y is the total cost.

Front

What is the total cost for riding 10 rides at an amusement park if the equation is y = 1.5x + 20?

Back

Total cost = 1.5(10) + 20 = 15 + 20 = $35.