AMPED 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 of 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 starting value of the dependent variable.

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 a pet store charges $5 to wash a cat and $7.50 to wash a dog, how can you represent the total cost of washing cats and dogs?

Back

Let c be the number of cats and d be the number of dogs. The equation is 5c + 7.5d = total cost.

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value(s) of the variable(s) that make the equation true.

Front

In the equation y = 3x + 10, what does the '10' represent?

Back

The '10' represents the monthly fee that Rich pays for his gym membership.

Front

In the equation y = 0.5x + 10, what does the '0.5' represent?

Back

The '0.5' represents the per-mile fee that Charlie pays for renting the moving truck.

Front

How do you determine the number of items rented from a total cost?

Back

Set up an equation based on the total cost, isolate the variable representing the number of items, and solve for that variable.

Front

If a video store charges $10 for a rental card plus $2 per movie, how would you express the total cost?

Back

Let m be the number of movies rented. The total cost is 10 + 2m.