TOPIC

Applications of linear equations

MY PROGRESS

Pug Score

0%

Best Streak

0 in a row

Study Points

+0

Overview

Practice

Watch

Read

Quiz

Next Steps

Get Started

Get unlimited access to all videos, practice problems, and study tools.

Try Now
Unlimited practice
Full videos

Back to Menu

Topic Progress

Pug Score

0%

Videos Watched

0/0

Best Practice

No score

Read

Not viewed

Best Quiz

No attempts

Best Streak

0 in a row

Study Points

+0

Read

Linear Equation Applications

A linear equation application models a real quantity, like cost or distance, that starts at a fixed value and changes at a constant rate: y = mx + b. See a worked rental-cost example, learn to identify the starting value and rate in a word problem, and see other situations this setup models.

Applying linear equations to real situations

A linear equation application models a real quantity that changes at a constant rate with an equation of the form y = mx + b, where b is the starting (fixed) value and m is the rate of change per unit.

Worked example: rental cost

Renting equipment costs a flat $20 fee plus $5 per hour. Writing cost as a function of hours x gives cost = 20 + 5x. At x = 0 hours, the cost is $20 (just the fee); at x = 6 hours, the cost is 20 + 5(6) = $50.

A linear equation applied to a real cost The cost to rent equipment is 20 dollars fixed plus 5 dollars per hour, so cost equals 20 plus 5 times the number of hours. At 0 hours the cost is 20 dollars; at 6 hours the cost is 50 dollars, and the line between them is straight because the rate is constant. hours cost ($) (0, $20) (6, $50) cost = 20 + 5 × hours
Cost = 20 + 5 × hours: a fixed starting value plus a constant rate.

Because the rate ($5 per hour) never changes, the graph is a straight line — the defining feature of a linear relationship.

Recognizing the two parts

Every linear application has the same two pieces: a starting value (the y-intercept) and a constant rate (the slope). Reading which is which from a word problem is the same skill used in tables of values and in solving two-step linear equations once you know the total cost and need to find x.

Other applications

The same y = mx + b setup models simple interest, distance traveled at constant speed, or a tank draining at a constant rate — anywhere a quantity starts at some value and changes steadily, as explored further in introduction to linear equations.

Related lessons