Proportional relationships & graphs drills

A proportional relationship always graphs as a straight line through the origin \((0, 0)\). A straight line that misses the origin is not proportional.

• Find \(k\): pick any point \((x, y)\) on the line except the origin and divide: \(k = y \div x\). If the line passes through \((4, 10)\), then \(k = 10 \div 4 = 2.5\). The point \((1, k)\) is always on the line.
• Find another point: multiply the new \(x\) by \(k\). On the same line at \(x = 6\): \(y = 2.5 \times 6 = 15\).

Common traps:

• Dividing \(x\) by \(y\), which gives \(0.4\) instead of \(2.5\).
• Adding instead of multiplying. Going from \(x = 4\) to \(x = 6\) does not mean \(y\) goes from 10 to 12. In a proportional relationship, \(y\) grows by the same factor as \(x\).