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Drawing Linear Graphs

FoundationAQAEdexcelOCR

Get to grips with drawing linear graphs using these Foundation GCSE Maths practice questions. The worksheet focuses on plotting straight-line graphs and finding gradients, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Plot at least three points to draw an accurate straight line.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Topic overview

Drawing a linear graph means plotting points that satisfy an equation and joining them with a straight line. A table of values is the standard way to organise the work.

Choose several \(x\) values, substitute each into the equation, and record the matching \(y\) value. Three points is the practical minimum: two define the line and the third checks it.

If one point is out of line with the others, it is almost always an arithmetic slip rather than a genuine feature, since every linear equation gives a perfectly straight line. That built-in check is why plotting three points rather than two is worth the extra moment.

Revision notes

Building a table of values

Pick \(x\) values across the range of the axes, including negatives if the grid allows. Substitute each into the equation.

For \(y = 2x + 1\) with \(x = -1, 0, 1, 2\): the \(y\) values are \(-1, 1, 3, 5\).

Plotting and joining

Plot each coordinate pair, then draw a single straight line through them with a ruler, extending to the edges of the grid.

Do not join the points with short segments, and do not stop at the last point unless the question restricts the range.

Checking for errors

A point off the line means a substitution error. Recalculate that \(y\) value rather than drawing a bent line.

Negative \(x\) values are the usual culprit: for \(y = 2x + 1\) with \(x = -3\), the answer is \(-5\), not \(7\).

Key points

  • Use a table of values to organise the points.
  • Substitute each x value into the equation.
  • Plot at least three points as a check.
  • Join them with a single straight line using a ruler.
  • Extend the line across the grid.
  • A point off the line means an arithmetic error.

Worked examples

Example 1

Complete a table of values for \(y = 3x - 2\) when \(x = 0, 1, 2\).

Working

\[3(0) - 2 = -2\]substitute x = 0
\[3(1) - 2 = 1\]substitute x = 1
\[3(2) - 2 = 4\]substitute x = 2

Example 2

Find \(y\) when \(x = -2\) for the line \(y = 4x + 3\).

Working

\[4 \times -2 = -8\]multiply, keeping the negative
\[-8 + 3 = -5\]add the constant

Example 3

A student plots \((0, 1)\), \((1, 3)\) and \((2, 4)\) for \(y = 2x + 1\). Identify the error.

Working

\[2(2) + 1 = 5\]substitute x = 2 into the equation
\[(2, 5) \text{, not } (2, 4)\]the third point was calculated incorrectly

Common mistakes

  • Making sign errors with negative x values.

    For y = 2x + 1 with x = −3, the answer is −5. Multiply first, keeping the sign.

  • Joining points with short segments.

    A linear equation always gives one straight line drawn with a ruler.

  • Plotting only two points.

    A third point catches arithmetic errors that two points cannot reveal.

  • Stopping the line at the final point.

    Extend it across the grid unless the question limits the range.

Exam tips

  • Plot three points so an error shows up immediately.
  • Recalculate any point that does not sit on the line.
  • Use a ruler and a sharp pencil.
  • Take extra care substituting negative values.

Key terms

Table of values
A table pairing x values with their calculated y values.
Substitute
To replace a variable with a number.
Linear
Producing a straight line when graphed.
Plot
To mark a point on a grid.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.