Plot linear graphs

Objective. Plot straight lines accurately from tables of values.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Plotting a linear graph accurately means marking several points from a table of values on axes and joining them with a single straight ruled line. Calculate at least three coordinate pairs from the equation, plot each one precisely, then draw a line extending beyond the outer points. For y = x + 1, the points (0, 1), (1, 2) and (2, 3) all lie in a straight line, confirming the equation is linear. Always use a ruler and label the line with its equation.

Worked example

Which table of coordinates correctly plots points for the linear graph y = 2x − 1?

Options

(0, −1), (1, 1), (2, 3)
(0, 1), (1, 3), (2, 5)
(0, −1), (1, 0), (2, 1)
(0, 1), (1, 1), (2, 1)

1 $Substitute x = 0: y = 2(0) - 1 = -1$
2 $Substitute x = 1: y = 2(1) - 1 = 1$
3 $Substitute x = 2: y = 2(2) - 1 = 3$
4 $The correct points are (0, -1), (1, 1), (2, 3)$

Answer: (0, −1), (1, 1), (2, 3)

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Common mistake. Pupils sometimes plot only two points and join them without checking a third, missing arithmetic slips that make the line wrong. Always plot a third point to confirm all three lie exactly on one straight line.

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