Linear Equations 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 represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you write an equation from a word problem involving a fixed fee and a variable cost?

Back

Identify the fixed fee and the variable cost per unit. The equation will be in the form: Total Cost = Fixed Fee + (Variable Cost per Unit * Number of Units).

Front

In the problem 'Dexter's Gym charges a one-time registration fee of $40 and $20 each month', what is the equation that models this situation?

Back

20x + 40 = 340, where x is the number of months.

Front

How do you find the total cost in a word problem involving a service fee and a per-minute charge?

Back

The total cost can be found using the equation: Total Cost = Per Minute Charge * Minutes Used + Service Fee.

Front

What is the equation for Ace Telecommunications' monthly cost?

Back

c = 0.12m + 8, where c is the total cost and m is the number of minutes used.

Front

How do you calculate the total cost for a rental that charges a daily rate and a per-mile fee?

Back

Total Cost = Daily Rate + (Per Mile Charge * Number of Miles Driven).

Front

In the problem 'Bob's Plumbing charges $15 per hour plus a service fee of $40', what is the equation that models this situation?

Back

y = 15x + 40, where y is the total cost and x is the number of hours worked.

Front

What does the term 'fixed fee' mean in a word problem?

Back

A fixed fee is a constant charge that does not change regardless of the amount of service or product used.