Plotting graphs from a table of values
Maths · Key Stage 3 · The School
Building the table
For y = 2x + 1, pick some values of x, usually from −2 to 3, and work out y for each. When x = 0, y = 1. When x = 1, y = 3. When x = 2, y = 5. Write these as pairs of coordinates: (0, 1), (1, 3), (2, 5). Three points are the minimum; a fourth is a check.
Plotting and joining
Plot each pair on a grid, x first then y, same as any coordinate. Once three or more points are plotted, lay a ruler against them. If they are not in a straight line, one of your table values has an error — go back and recheck it before drawing anything. A straight line drawn through correct points can be extended in both directions, past the points you actually calculated.
Reading the graph both ways
A graph answers two kinds of question. Given an x-value, go up to the line and across to read y. Given a y-value, go across to the line and down to read x. Both directions use the same drawn line — you never need to recalculate from the equation once the line is drawn correctly.
For y = 3x − 2: when x = 0, y = −2. When x = 1, y = 1. When x = 2, y = 4. Plot (0, −2), (1, 1), (2, 4) and draw the line through them. Now use the graph, not the equation, to answer: what is y when x = 1.5? Go up from 1.5 on the x-axis to the line, then across to the y-axis — the line gives about 2.5. Check with the equation: 3(1.5) − 2 = 2.5. They match, which is exactly what a correctly drawn line should do.