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 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 starting point of the line on the y-axis.

Front

How do you write an equation from a word problem?

Back

Identify the variables, determine the relationship between them, and translate the words into a mathematical equation.

Front

If a car rental charges $8.50 per hour plus a $25.50 fee, how do you express the total cost for x hours?

Back

The total cost can be expressed as y = 25.5 + 8.5x.

Front

What does it mean if the slope of a cost equation is positive?

Back

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

Front

How can you find the amount left in an account after spending a fixed amount daily?

Back

You can use the equation y = initial amount - (daily spending * number of days).

Front

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

Back

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

Front

In the equation y = -2x + 40, what does the -2 represent?

Back

The -2 represents the amount of money Sonya spends each day on lunch, indicating a decrease in her account balance.

Front

How do you determine the total cost for multiple children in a camp with a base fee?

Back

You can use the equation y = additional fee per child * number of additional children + base fee.