Worksheets › Class 9 › Two Variables, One Line › Cheat sheet
Class 9 Two Variables, One Line: cheat sheet
CBSE Mathematics. An equation ax + by + c = 0 has infinitely many solutions, and they all lie on one straight line.
Key ideas
- A linear equation in two variables is ax + by + c = 0 with a and b not both 0.
- A solution is a pair (x, y) that makes the equation true; there are infinitely many.
- To find solutions, choose a value of x and work out y.
- Every solution is a point on the graph, which is a straight line; every point on the line is a solution.
- x = k is a line parallel to the y-axis; y = k is parallel to the x-axis.
- To check a point, substitute it: it lies on the line only if both sides are equal.
Remember
| General form | ax + by + c = 0 |
| Where the line meets the y-axis | put x = 0 |
| Where the line meets the x-axis | put y = 0 |
| Fare-type rule | y = fixed charge + rate × x |
Watch out
- Saying the equation has only one solution.
- Swapping x and y when plotting a point.
- Forgetting that the first unit may be charged differently (y = 46 + 16(x − 1)).
Worked example
A taxi charges Rs 46 for the first km and Rs 16 for every km after that. Write an equation for the fare y for x km, and find the fare for 12 km.
Working: y = 46 + 16(x − 1) = 16x + 30; y = 16 × 12 + 30 = 222
Answer: y = 16x + 30; Rs 222
Practise Two Variables, One Line
Revise with this page, then practise: every Two Variables, One Line sheet in the app is new, with an answer key and working.
Coming soon for Android and iPhone.