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Linear Equations
These problems involve the use of linear equations or expressions in the form ax + b. Various linear topics, such as slope, intercepts and graphing may come into play.

Some of these problems are also in the following subcategories:

Related Resources
Interactive resources from our Math Tools project:
   Algebra: Linear Equations
The closest match in our Ask Dr. Math archives:
   High School: Linear Equations
NCTM Standards:
   Algebra Standard for Grades 9-12

Access to these problems requires a Membership.

Are You Positive? - Steve Risberg
Algebra, difficulty level 3. Find all values of x that make a rational expression have a positive value. ... more>>

At Least This Many - Terry Trotter
Algebra, difficulty level 2. Using two data points from the NBA statistics chart, form an equation (y = mx + b style), then use it to predict other data points. ... more>>

Battle of the Bands - Terry Trotter
Algebra, difficulty level 3. Students at Rahkenrole High School vote to decide which band should play at the end-of-year dance. After some students change their minds about which band to vote for, the result is a tie. Can you figure out how many students voted? ... more>>

Bowl-O-Rama! - Steve Risberg
Algebra, difficulty level 1. Given information about the number of games two people bowled and how much each paid, determine the cost of bowling at Bowl-O-Rama. ... more>>

Building a Bakery - Steve Risberg
Algebra, difficulty level 3. Find the best place to build the bakery so that the delivery miles to the stores are minimized. ... more>>

Buried Treasure - Steve Risberg
Algebra, difficulty level 3. The pirate Algebeard has drawn an unusual treasure map. Can you determine where his treasure is buried? ... more>>

Capture the Flag! - Steve Risberg
Algebra, difficulty level 4. Help the Algebra and Geometry classes at Mathland High find the equation of a perpendicular bisector to fairly divide the woods for their game of Capture the Flag. ... more>>

Choosing Charity - Steve Risberg
Algebra, difficulty level 2. A company donates to a relief fund by giving a certain amount plus an additional amount for each employee who decides to donate. Given two data points, find the linear equation that defines the company's part of the total donation. ... more>>

Crossed Wires - Steve Risberg
Algebra, difficulty level 3. Guy wires support two poles of different heights. Find the height of their intersection and explore what happens as the distance between the poles changes. ... more>>

Examining an Equation - Steve Risberg
Algebra, difficulty level 2. Find integer solutions to an equation in two variables. ... more>>

Finding a Two-Digit Number - Annie Fetter
Algebra, difficulty level 2. Find a two-digit number such that if you reverse its digits to get another two-digit number, then add this to the original number, you get 143. ... more>>

From Here to There - Steve Risberg
Algebra, difficulty level 2. Given descriptions of the rate schedules of a bus, a taxi, and a shuttle, choose the graphs that best illustrate the cost of riding each one. ... more>>

Heating the Tub - Steve Risberg
Algebra, difficulty level 1. Water in a hot tub is heated. Given two times and the temperature at those times, find an equation that models the heating process, then use it to predict temperatures and times as the heating continues. ... more>>

Hiking Mount Hood - PoW staff
Algebra, difficulty level 1. Don hikes up and down a mountain at various speeds. Choose the graph that best represents his trip. ... more>>

Hole in One! - Steve Risberg
Algebra, difficulty level 4. Given the dimensions of a miniature golf hole, use slopes to determine how Tiger needs to hit his shot to make a hole in one. ... more>>

Holiday Dance - Steve Risberg
Algebra, difficulty level 2. Two bands are being considered for the holiday dance at Rahkenrole High School. Each band charges a base fee and an hourly rate. Help the Student Council compare the bands and find the best deal. ... more>>

Home-Made Valentine Card - Terry Trotter
Algebra, difficulty level 2. Reuben expresses his affection for his girlfriend by making his own Valentine's Day card, described mathematically. ... more>>

Illuminating Lines - Annie Fetter
Algebra, difficulty level 2. Match up statements, equations, and sets of points on coordinate planes. ... more>>

Laser Tag - Steve Risberg
Algebra, difficulty level 3. Help Karsten determine where he needs to shoot his laser in order to hit his friend Jorge in a game of laser tag. ... more>>

Line Logic - Steve Risberg
Algebra, difficulty level 1. Given five statements, find an equation of a line that makes four of the statements true and one false. ... more>>

Marsha's Triangle - Marsha Hurwitz
Algebra, difficulty level 3. Find the area of an isosceles triangle whose two legs are on the x and y axes and whose hypotenuse passes through the point (c,d). ... more>>

Math on the Midway - Steve Risberg
Algebra, difficulty level 1. Can you win the carnival midway math game by finding a pattern in the numbers? ... more>>

Phone-O-Graph Phollies - Bill Graham
Algebra, difficulty level 2. Students are asked to use algebra to compare three telephone calling plans to determine at what number of calls each plan would be preferable. ... more>>

A Phone-y Deal? - Steve Risberg
Algebra, difficulty level 2. Compare two cell phone pricing plans to determine for how many minutes of calls per month each one is the better deal. ... more>>

Reverse It! - Annie Fetter Steve Risberg
Algebra, difficulty level 1. Find a two-digit number such that when you reverse the digits and add the new number to the original one, the sum is 154. ... more>>

Sam and Teri's Bank Accounts - Terry Trotter
Algebra, difficulty level 1. Sam and Teri have bank accounts. Sam always withdraws money; Teri always saves it. When will they have equal balances, or will they? ... more>>

Skeeball Showdown - Steve Risberg
Algebra, difficulty level 3. Kira and Daquan each play a game of Skeeball to see who gets the higher score. Given descriptions of their results in relation to each other, determine the final score of their match and how many balls each player rolled. ... more>>

Spell It Out - Steve Risberg Annie Fetter
Algebra, difficulty level 2. A word-find problem exploring how sets of points that form lines can be described by written sentences. An introduction to linear equations that sets the stage for the standard y = mx + b form. ... more>>

The Spider and the Fly - J. A. H. Hunter
Algebra, difficulty level 2. A spider presents a challenge to a fly: solve a math problem and escape! ... more>>

Splitting a Square - Terry Trotter
Algebra, difficulty level 3. A square is drawn on a coordinate plane with vertices P(1, 0), Q(2, 0), R(2, 1) and S(1, 1). A line is drawn from the origin that cuts the square into two sections whose areas are in a ratio of 2:1. What's the equation of the "cutting" line? ... more>>

A Tale of Two Intercepts - Terry Trotter
Algebra, difficulty level 3. Find the distance between two y-intercepts. ... more>>

Taxi! - Steve Risberg
Algebra, difficulty level 1. Taxi fares in Lineville are based on a linear equation. Given the costs and distances of two rides, find the equation and use it to answer several questions. ... more>>

Texting 1, 2, 3 - Steve Risberg
Algebra, difficulty level 2. Determine the pricing of Kheri's cell phone texting plan. ... more>>

The Coordinate Carousel - Steve Risberg
Algebra, difficulty level 3. Mrs. Nomial is watching her daughters on the carousel and notices something interesting. Determine how far away from the edge of the carousel she is standing. ... more>>

To B or Not To B - Steve Risberg
Algebra, difficulty level 2. Given a letter pattern, find expressions for the number of B's and the ratio of B's to total letters in the nth term. ... more>>

Triangle Possibilities - Steve Risberg
Algebra, difficulty level 2. Given information about side lengths of a triangle, determine possible dimensions. ... more>>

Triangle Probability - Annie Fetter
Algebra, difficulty level 3. A point is randomly selected from within a triangle with vertices at (0,0), (0,4) and (6,0). What is the probability that the x-coordinate of the selected point is less than the y-coordinate? ... more>>

A Triangle's Area - Canadian Open Math Challenge 1999 via Tim Lang
Algebra, difficulty level 3. Find the "b" values of two lines needed to form two congruent triangles of a given area. ... more>>

What's the Temperature - Annie Fetter
Algebra, difficulty level 1. At what temperature do you get the same answer, regardless of whether you use the Fahrenheit or the Celsius scale? ... more>>

X Marks the Spot - Terry Trotter
Algebra, difficulty level 3. A Spanish pirate buries his treasure on an island in a very mathematical manner. Can you locate the "X" spot? ... more>>

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