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Linear Equations
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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
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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.
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At Least This Many
- Terry Trotter
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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
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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?
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Buried Treasure
- Steve Risberg
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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
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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
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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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Finding a Two-Digit Number
- Annie Fetter
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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.
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Heating the Tub
- Steve Risberg
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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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Holiday Dance
- Steve Risberg
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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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Home-Made Valentine Card
- Terry Trotter
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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
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Algebra, difficulty level 2. Match up statements, equations, and sets of points on coordinate planes.
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Marsha's Triangle
- Marsha Hurwitz
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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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Phone-O-Graph Phollies
- Bill Graham
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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 Phone-y Deal?
- Steve Risberg
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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
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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.
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Sam and Teri's Bank Accounts
- Terry Trotter
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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
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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
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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.
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The Spider and the Fly
- J. A. H. Hunter
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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
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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
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Algebra, difficulty level 3. Find the distance between two y-intercepts.
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Taxi!
- Steve Risberg
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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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The Coordinate Carousel
- Steve Risberg
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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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Triangle Probability
- Annie Fetter
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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?
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A Triangle's Area
- Canadian Open Math Challenge 1999 via Tim Lang
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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
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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
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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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