Sheet № 91 · Foundation + Higher · AQA · Edexcel · OCR
Plotting Straight-Line Graphs –
Plotting straight-line graphs is a core skill tested on both Foundation and Higher tier GCSE Maths papers. Understanding the connection between an equation like y = mx + c and its graph allows you to tackle gradient questions, simultaneous equations, and real-life modelling problems.
§Key definitions
Question:
Draw the graph of y = 2x + 1 for values of x from -2 to 3.
Answer:
A straight line through the points listed above, crossing the y-axis at (0, 1).
Q1 (Foundation):
Complete the table of values for y = 3x - 2 when x = -1, 0, 1, 2, 3.
Q2 (Foundation):
Write down the gradient and y-intercept of y = -2x + 5.
Q3 (Higher):
Find the equation of the line passing through (2, 3) and (6, 11) in the form y = mx + c.
§Formulas to memorise
y = mx + c, where m = gradient and c = y-intercept
Gradient = change in y / change in x = (y2 - y1) / (x2 - x1)
Table of values method: — choose at least three x values (e.g. -2, 0, 2), substitute each into the equation, and calculate y.
Gradient-intercept method (alternative): — mark the y-intercept (0, c) on the y-axis, then from that point move across 1 unit and up or down by m units to place a second point. Draw the line through both points.
If the equation is not in y = mx + c form, rearrange it.
Worked example
Draw the graph of y = 2x + 1 for values of x from -2 to 3.
Working:
⚠ Common mistakes
- ✗Plotting points inaccurately. A tiny error in placing a point makes the line wrong. Use the grid lines carefully and double-check each coordinate before drawing.
- ✗Not using a ruler. Straight-line graphs must be drawn with a ruler. A freehand line will not pass through all your points and costs marks.
- ✗Confusing gradient and y-intercept. In y = 3x + 2, the gradient is 3 (the coefficient of x) and the y-intercept is 2 (the constant). Students sometimes swap them.
✦ Exam tips
- →Always plot at least three points when using the table of values method. If one point is slightly wrong, the other two will reveal the error because all three must lie on a straight line.
- →Extend your line to fill the grid. A short line segment in the middle of the axes can lose marks if the question asks you to "draw the graph."
- →If the equation is given in a different form (e.g. 3x + y = 7), rearrange to y = mx + c before trying to identify the gradient and intercept.