Linear Equations - Word Problems - mixed

Front

What is the slope in a linear equation?

Back

The slope represents the rate of change in a linear equation, indicating how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

In the equation y = mx + b, what do m and b represent?

Back

m represents the slope of the line, and b represents the y-intercept, which is the value of y when x = 0.

Front

How do you calculate the total cost from a linear equation?

Back

Substitute the value of x (the independent variable) into the equation to find the corresponding value of y (the total cost).

Front

What does the y-intercept indicate in a word problem involving costs?

Back

The y-intercept indicates the initial cost or fixed fee before any variable costs are added.

Front

If a gym membership costs $50 per month, what is the slope of the cost equation?

Back

The slope is $50, representing the monthly cost increase.

Front

How can you represent a situation where a person spends a fixed amount each month from a gift card?

Back

Use the equation y = -mx + b, where m is the amount spent each month, and b is the initial amount on the gift card.

Front

What is the equation for a cost that includes a delivery fee?

Back

The equation is y = mx + b, where m is the cost per item (or person), and b is the fixed delivery fee.

Front

How do you find the number of months a membership was paid for if you know the total cost?

Back

Rearrange the equation y = mx + b to solve for x: x = (y - b) / m.

Front

What does a negative slope indicate in a word problem?

Back

A negative slope indicates a decrease in the dependent variable as the independent variable increases.

Front

If a meal costs $12.50 per person plus a delivery fee, how would you express this as a linear equation?

Back

The equation is y = 12.5x + 30, where x is the number of people.