Linear Equations from 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 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

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

Back

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

Front

If a tank releases water at a rate of 25 gallons per minute and starts with 120 gallons, what is the equation for the amount of water left after x minutes?

Back

y = 120 - 25x.

Front

What is the equation for the total cost of joining an online learning community with a $20 startup fee and a $5 monthly fee?

Back

y = 5x + 20, where x is the number of months.

Front

How do you determine the total cost of a holiday meal that costs $12.50 per person plus a $30 delivery fee?

Back

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

Front

What is the equation for Jerry's total money after working x hours if he starts with $20 and earns $7 per hour?

Back

y = 7x + 20.

Front

What does it mean if a linear equation has a negative slope?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.