Direct Variation
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 46 of 54.
Apples cost the same per kilo. 5 kilos cost 15 dollars and 10 kilos cost 30. Double the weight and the price doubles: the price varies directly with the weight.
In symbols, y = kx, where k is a fixed number called the constant of variation. To find it, divide one y by its x: k = 15/5, which is 3. So the rule is y = 3x, 3 dollars a kilo, and 7 kilos cost 21 dollars.
The ratio y/x is the same for every pair, which is how you spot direct variation in a table. Its graph is a line through (0, 0) with slope k: no apples cost nothing.
Challenge
y varies directly with x, and y is 24 when x is 6. Find the constant k. On the blank board, write k = ... as a fraction on the first line, then work it out on the next.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Polynomials & Rational Expressions
1Polynomial Long Division
How Long Division WorksOne Term at a TimeA Remainder Left OverA Missing TermDividing by a QuadraticRecap: Long Division7Adding and Subtracting
Same BottomDifferent BottomsSubtractingFactor the Bottoms FirstRecap: Adding Fractions2Remainders and Factors
The Remainder TheoremThe Factor TheoremFinding a Missing NumberUsing a Known FactorRecap: Remainders and Factors5Sign Charts
Between the RootsOutside the RootsA Negative Leading TermReading a Sign ChartRecap: Sign Charts