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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 912
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.
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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.
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Battle of the Bands
 Terry Trotter

Algebra, difficulty level 3. Students at Rahkenrole High School vote to decide which band should
play at the endofyear 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?
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BowlORama!
 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 BowlORama.
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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.
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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?
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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.
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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.
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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.
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Examining an Equation
 Steve Risberg

Algebra, difficulty level 2. Find integer solutions to an equation in two variables.
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Finding a TwoDigit Number
 Annie Fetter

Algebra, difficulty level 2. Find a twodigit number such that if you reverse its digits to get another twodigit number, then add this to the original number, you get 143.
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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.
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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.
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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.
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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.
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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.
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HomeMade 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.
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Illuminating Lines
 Annie Fetter

Algebra, difficulty level 2. Match up statements, equations, and sets of points on coordinate planes.
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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.
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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.
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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).
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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?
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PhoneOGraph 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.
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A Phoney 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.
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Reverse It!
 Annie Fetter Steve Risberg

Algebra, difficulty level 1. Find a twodigit number such that when you reverse the digits and add
the new number to the original one, the sum is 154.
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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?
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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.
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Spell It Out
 Steve Risberg Annie Fetter

Algebra, difficulty level 2. A wordfind 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.
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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!
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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?
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A Tale of Two Intercepts
 Terry Trotter

Algebra, difficulty level 3. Find the distance between two yintercepts.
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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.
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Texting 1, 2, 3
 Steve Risberg

Algebra, difficulty level 2. Determine the pricing of Kheri's cell phone texting plan.
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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.
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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.
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Triangle Possibilities
 Steve Risberg

Algebra, difficulty level 2. Given information about side lengths of a triangle, determine possible dimensions.
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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 xcoordinate of the selected point is less than the ycoordinate?
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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.
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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?
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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?
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