Linear Equation 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 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 is the point where the line crosses the y-axis.

Front

How do you write an equation for a word problem involving a total cost?

Back

Identify the fixed costs and variable costs, then use the equation format y = mx + b, where m is the variable cost per unit and b is the fixed cost.

Front

If a hamburger costs $8.90 and each topping costs $1.40, how would you express the total cost?

Back

The total cost can be expressed as y = 1.40x + 8.90, where x is the number of toppings.

Front

What does the variable 'x' typically represent in a linear equation?

Back

In a linear equation, 'x' usually represents the independent variable, which is the quantity that can change.

Front

What does the variable 'y' typically represent in a linear equation?

Back

In a linear equation, 'y' usually represents the dependent variable, which is the quantity that depends on the value of 'x'.

Front

How can you determine the number of days Sonya can eat lunch with $40 if each lunch costs $2?

Back

You can use the equation y = -2x + 40, where y is the amount left after x days.

Front

What is the equation for the total cost of a holiday meal for x people, given a cost of $12.50 per person and a $30 delivery fee?

Back

The equation is y = 12.5x + 30.

Front

In the context of a problem, what does it mean if the slope is positive?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases.