Graphing Points from a Rule (Grades 6–8)
A rule like "y = x + 2" connects each x to a y. To find points on the line, pick x-values, apply the rule, and pair them: x = 0 → y = 2, x = 1 → y = 3, x = 2 → y = 4, giving (0, 2), (1, 3), (2, 4).
Understanding graphing points from a rule
Plotting these shows the line the rule describes; testing a point means checking whether it makes the rule true.
Seeing it in action
Worked example
Find two points on y = x + 2.
x = 0 → y = 2 gives (0, 2). x = 3 → y = 5 gives (3, 5). → (0, 2) and (3, 5).
Each point fits y = x + 2.
A common mistake, and the fix
Swapping x and y in a point.
On y = x + 2, x = 1 gives y = 3, so the point is (1, 3), not (3, 1). Check a point by putting its first number into the rule: for (3, 1), 3 + 2 = 5, not 1, so that point isn’t on the line.
Try a few
On y = 2x, what is y when x = 4?
→ (4, 8)
Is (2, 5) on y = x + 3?
2 + 3 = 5.
On y = x − 1, the point at x = 6?
6 − 1 = 5.
Coordinate Quest
A calm treasure-map game for plotting, reading, and translating points on a coordinate plane.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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