[discia] GCSE Maths › Algebra › Drawing Linear Graphs

Drawing Linear Graphs

discia.org 10 questions · 26 marks
Name Date
  1. Either paper 2 marks

    A straight line is drawn on the grid.

    xy-6-5-4-3-2123456-8-7-6-5-4-3-2123456780
    (a)

    Use the graph to write down the value of \(y\) when \(x = 4\).

    (b)

    Use the graph to write down the value of \(x\) when \(y = -7\).

    Show answer
    (a) \(-6\)
    (b) \(5\)
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  2. Either paper 2 marks

    Each grid has \(x\) and \(y\) from \(-6\) to \(6\).

    (a)

    On this grid, draw the line with equation \(y = -4\)

    xy-6-5-4-3-2123456-6-5-4-3-2-11234560
    (b)

    On this grid, draw the line with equation \(x = 5\)

    xy-6-5-4-3-2123456-6-5-4-3-2-11234560
    Show answer
    (a) A horizontal line through \((0, -4)\), \((1, -4)\) and every other point with \(y = -4\)
    (b) A vertical line through \((5, 0)\), \((5, 1)\) and every other point with \(x = 5\)
    (a)xy-6-5-4-3-2123456-6-5-4-3-2-11234560
    (b)xy-6-5-4-3-2123456-6-5-4-3-2-11234560
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  3. Either paper 3 marks
    The table shows some values of \(y = 2x - 1\)
    x-3-2-101
    y-51
    Three of the \(y\) values are missing.
    (a)

    Work out the value of \(y\) when \(x = 0\).

    (b)

    Work out the value of \(y\) when \(x = -3\).

    (c)

    Work out the value of \(y\) when \(x = -1\).

    Show answer
    (a) \(-1\)
    (b) \(-7\)
    (c) \(-3\)
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  4. Either paper 2 marks

    Here are four points.

    \((-2, -4) \qquad (2, 8) \qquad (4, 12) \qquad (3, 8)\)

    One of them lies on the line \(y = 3x - 1\)

    Write down the coordinates of that point.

    Show answer
    \((3, 8)\)
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  5. Either paper 3 marks

    Each grid below has one straight line drawn on it.

    (a) xy-7-6-5-4-3-21234567-7-6-5-4-3-212345670

    Write down the equation of the line drawn on this grid.

    (b) xy-7-6-5-4-3-21234567-7-6-5-4-3-212345670

    Write down the equation of the line drawn on this grid.

    (c)

    Suppose both lines were drawn on the same grid.

    Write down the coordinates of the point where they would cross.

    Show answer
    (a) \(y = 2\)
    (b) \(x = 3\)
    (c) \((3, 2)\)
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  6. Either paper 2 marks

    You are going to draw the graph of \(y = -x - 2\) on this grid, for values of \(x\) from \(-4\) to \(4\).

    xy-7-6-5-4-3-21234567-7-6-5-4-3-212345670

    The quickest way to draw a straight line is to work out the two end points, plot them and join them up.

    (a)

    Find the coordinates of the point you would plot for \(x = -4\).

    (b)

    Find the coordinates of the point you would plot for \(x = 4\).

    Show answer
    (a) \((-4, 2)\)
    (b) \((4, -6)\)
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  7. Either paper 3 marks

    On the grid, draw the graph of \(y = -2x + 3\) for values of \(x\) from \(-4\) to \(4\).

    xy-4-224-10-9-8-7-6-5-4-3-2123456789100
    Show answer
    A straight line through \((0, 3)\) and \((1, 1)\)
    xy-4-224-10-9-8-7-6-5-4-3-2123456789100
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  8. Either paper 4 marks
    The table gives some values of \(y = -x - 4\)
    x-10123
    y-3-5-6
    Two of the \(y\) values are missing.
    (a)

    Work out the value of \(y\) when \(x = 0\).

    (b)

    Work out the value of \(y\) when \(x = 3\).

    (c)

    On the grid, plot the five points from the table and join them with a straight line, for values of \(x\) from \(-1\) to \(3\).

    xy-4-2246-10-9-8-7-6-5-4-3-2123456789100
    Show answer
    (a) \(-4\)
    (b) \(-7\)
    (c) Points at \((-1, -3)\), \((0, -4)\), \((1, -5)\), \((2, -6)\) and \((3, -7)\), joined by one straight line
    (c)xy-4-2246-10-9-8-7-6-5-4-3-2123456789100
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  9. Either paper 3 marks

    A straight line is drawn on the grid. Both axes are numbered in twos, so each square is worth \(2\).

    The dashed lines show one reading being taken.

    xy-10-8-6-4-2246810-10-8-6-4-22468100
    (a)

    Use the graph to write down the value of \(y\) when \(x = 6\).

    (b)

    Use the graph to work out the value of \(x\) when \(y = -6\).

    Show answer
    (a) \(4\)
    (b) \(-4\)
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  10. Either paper 2 marks
    A student has filled in a table of values for \(y = 2x + 5\)
    x-3-2-101
    y-11355
    One of the \(y\) values is wrong.
    (a)

    Write down the value of \(x\) for the entry that is wrong.

    (b)

    Write down the correct value of \(y\) for that entry.

    Show answer
    (a) \(1\)
    (b) \(7\)
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discia.org Drawing Linear Graphs · sheet 1
Answers Drawing Linear Graphs · sheet 1
  1. (a) \(-6\)
    (b) \(5\)
  2. (a) A horizontal line through \((0, -4)\), \((1, -4)\) and every other point with \(y = -4\)
    (b) A vertical line through \((5, 0)\), \((5, 1)\) and every other point with \(x = 5\)
    (a)xy-6-5-4-3-2123456-6-5-4-3-2-11234560
    (b)xy-6-5-4-3-2123456-6-5-4-3-2-11234560
  3. (a) \(-1\)
    (b) \(-7\)
    (c) \(-3\)
  4. \((3, 8)\)
  5. (a) \(y = 2\)
    (b) \(x = 3\)
    (c) \((3, 2)\)
  6. (a) \((-4, 2)\)
    (b) \((4, -6)\)
  7. A straight line through \((0, 3)\) and \((1, 1)\)
    xy-4-224-10-9-8-7-6-5-4-3-2123456789100
  8. (a) \(-4\)
    (b) \(-7\)
    (c) Points at \((-1, -3)\), \((0, -4)\), \((1, -5)\), \((2, -6)\) and \((3, -7)\), joined by one straight line
    (c)xy-4-2246-10-9-8-7-6-5-4-3-2123456789100
  9. (a) \(4\)
    (b) \(-4\)
  10. (a) \(1\)
    (b) \(7\)
discia.org Drawing Linear Graphs · sheet 1