Plotting graphs
From equation to table
A graph question nearly always starts with a table of values. Work out y for each x, one column at a time.
- write the equation with y on its own: 2y = 3x − 2 becomes y = (3x − 2) ÷ 2
- put each x in brackets when it is negative: x = −2 gives y = (3 × (−2) − 2) ÷ 2 = −4
- for x², square first: (−3)² = 9, never −9
- check the pattern: a straight line goes up or down by the same amount each step
The usual slip: (−3)² typed into a calculator as −3² gives −9. Use the brackets.
Plotting and joining
Plot each point as a small cross, to within half a small square. Then join the points the way the equation says:
- a straight line (y = mx + c, or ax + by = c) with a ruler, right across the grid;
- a curve (x², x³, k/x, 2^x) with one smooth curve through every point, never with straight pieces between them.
A quadratic is symmetrical, so its lowest point sits halfway between two points with the same y value. If one point breaks the pattern, recheck it before you draw.
Reading answers from your graph
Once the graph is drawn, it answers questions.
- x² − 4x + 1 = 0: read the x values where the curve crosses the x-axis (y = 0)
- x² − 4x + 1 = 4: draw the line y = 4 and read the x values where it meets the curve
- a value off the end of a straight-line graph: read a value you can reach, then scale it up
Give a reading to the accuracy the grid allows, usually 1 decimal place. A mark scheme accepts a small range either side of the true value.
This question is in Brainlag Plus