A table shows (2, 7), (4, 14), (6, 21). Is it proportional?
- 7/2 = 14/4 = 21/6 = 3.5.
- The constant ratio is 3.5, so y = 3.5x.
- The proportional model includes (0, 0).
Proportional tables & graphs
A constant ratio connects every representation.
Look for a constant quotient
For a proportional relationship y = kx, y/x is the same for every nonzero x. The constant k is the amount of y per 1 x-unit. Equal differences alone are not enough.
See the quantities change.
Predict before changing a value. The written explanation below remains available without JavaScript.
The graph passes through the origin
A proportional relationship has y = 0 when x = 0. Its graph lies on a straight line through (0, 0). A straight line with a nonzero starting charge is linear but not directly proportional.
Keep the context in the graph
Label axes and units. Separate points can represent whole ticket counts; measured quantities such as elapsed time may allow a continuous line. The line is meaningful only over the situation’s valid domain.
Khan Academy
Pause the explanation before a calculation. Predict the next step and explain which quantities are being compared.
Worked examples
A taxi costs $5 plus $2 per kilometre. Is cost proportional to distance?
- C = 2d + 5.
- At d = 0, C = 5, not 0.
- The cost changes linearly but C/d is not constant. It is not directly proportional.
Try it before checking.
For y = 4x, what point represents x = 3?
A first hint
Multiply the x-value by the constant ratio.
Compare your reasoning
y = 12; the point is (3, 12).
Practise the skill.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
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Explain a little more.
Why should a ticket-price graph use points at whole ticket counts?
Use this thinking in the If… project →