IGCSE Maths / Graphs of straight lines
Drawing a straight line from a table of values revision notes
Edexcel International GCSE Maths (4MA1), chapter 6: Graphs of straight lines, specification point 3.3i-f. Free lesson.
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To draw a straight-line graph, substitute each given x value into the equation, then plot the resulting coordinate pairs and join them with a ruler. Checking that the points line up helps you spot errors in your table.
How to make a table of values
A table of values pairs each x value with the y value it produces. Substitute each x value into the equation, which means putting it in place of x, then calculate y. For a linear equation such as y = 2x + 1, the y values rise by 2 whenever x rises by 1, because 2 is the number in front of x. Work through every x value given, even though two points are enough to draw a line. Extra points help you check your answers.
How to plot and join the points
Each pair from the table gives a point on the graph. Plot the x coordinate first, then the y coordinate. If the table is correct, all the points lie on the same straight line. Use a ruler to draw the line and extend it a little past the end points. A freehand line can lose the accuracy mark, even if your table is correct. The end points can help you see the full line, but plot every pair in the table.
How the line shows the equation
For y = 2x + 1, the points (−1, −1) and (3, 7) are four steps apart horizontally and eight vertically. The gradient is the vertical change divided by the horizontal change, so it is 8 ÷ 4 = 2. This matches the 2 in the equation: each step across raises y by 2. The line crosses the vertical axis at (0, 1), matching the number added in the equation.
How to spot a wrong point
A linear equation of the form y = mx + c always gives a straight line. If one plotted point sits away from the others, recheck its y value in the table. Do not draw a bent line through it: a bend means the point or table is wrong. Two points determine a straight line, but they cannot show whether either point is wrong. A third point that lines up provides a useful check.
A second table to check
For y = 3x − 2, the y values rise by 3 each time x rises by 1. This matches the number in front of x and gives another check on the calculations. For x = −1, 0, 1, 2, the corresponding y values are −5, −2, 1, 4.