Plotting straight-line graphs

The Maths Habit

One cross is out of line with the others. Which one?

ABCDEC. A ruler goes through the other four.

Write the coordinates of P.123451234560xyP(3, 5)
y = x + 3Work out y when x = 4y = 7

y = …
Rule
It tells you how to work out y from x.
xy
Table of values
A table of x values and the y value that goes with each one.
1234512340xy
Plot
Mark a point on a grid with a cross.
1234512340xy
Linear graph
A graph that is a straight line.

y = x + 4

x01234y123451234567891011120xy45678
  1. 1Work out each y.Put each x into the rule.
  2. 2Plot each point.Each column is a point. Go across to x, then up to y.
  3. 3Join with a ruler.The points make a straight line.

Draw the graph of y = x + 6.

x01234y123451234567891011120xy678910
1Work out each y.
2Plot each point.
3Join with a ruler.
(0, 6)(1, 7)(2, 8)(3, 9)(4, 10)

Draw the graph of y = x + 7.

x01234y7891011123451234567891011120xy
1Work out each y.
2Plot each point.
3Join with a ruler.
(0, 7)(1, 8)(2, 9)(3, 10)(4, 11)

Draw the graph of y = x + 6.

x01234y123451234567891011120xy678910
1Work out each y.
2Plot each point.
3Join with a ruler.
(0, 6)(1, 7)(2, 8)(3, 9)(4, 10)
1Work out each y.
2Plot each point.
3Join with a ruler.

Draw the graph of y = x + 8.

x0123y891011123451234567891011120xy
(0, 8)(1, 9)(2, 10)(3, 11)

Draw the graph of y = x + 6.

x01234y123451234567891011120xy678910
1Work out each y.
2Plot each point.
3Join with a ruler.
(0, 6)(1, 7)(2, 8)(3, 9)(4, 10)
1Work out each y.
2Plot each point.
3Join with a ruler.

Draw the graph of y = x.

x01234y01234123451234567891011120xy
(0, 0)(1, 1)(2, 2)(3, 3)(4, 4)

Draw the graph of y = x + 6.

x01234y123451234567891011120xy678910
1Work out each y.
2Plot each point.
3Join with a ruler.
(0, 6)(1, 7)(2, 8)(3, 9)(4, 10)
1Work out each y.
2Plot each point.
3Join with a ruler.

Draw the graph of y = 3x.

x123y123451234567891011120xy369
(1, 3)(2, 6)(3, 9)

Copy and complete each table.

1

y = x + 9

x012
y91011
2

y = 2x

x1234
y2468
3

y = x + 2

x1234
y3456
1Work out each y.
2Plot each point.
3Join with a ruler.

x = 3. What is 2x?

2x
2365
6, because 2x means 2 × x

y = 2x + 3

x01232xy123451234567891011120xy02463579
  1. 1Work out each y.Times first: the 2x row. Then add 3: the y row.
  2. 2Plot each point.Each column is a point (x, y).
  3. 3Join with a ruler.The points make a straight line.

Draw the graph of y = 2x + 2.

x12342xy123451234567891011120xy246846810
1Work out each y.
2Plot each point.
3Join with a ruler.
(1, 4)(2, 6)(3, 8)(4, 10)

Draw the graph of y = 3x + 1.

x1233x369y123451234567891011120xy4710
1Work out each y.
2Plot each point.
3Join with a ruler.
(1, 4)(2, 7)(3, 10)

Draw the graph of y = 2x + 2.

x12342xy123451234567891011120xy246846810
1Work out each y.
2Plot each point.
3Join with a ruler.
(1, 4)(2, 6)(3, 8)(4, 10)
1Work out each y.
2Plot each point.
3Join with a ruler.

Draw the graph of y = 2x + 6.

x0122x024y123451234567891011120xy6810
(0, 6)(1, 8)(2, 10)

Draw the graph of y = 2x + 2.

x12342xy123451234567891011120xy246846810
1Work out each y.
2Plot each point.
3Join with a ruler.
(1, 4)(2, 6)(3, 8)(4, 10)
1Work out each y.
2Plot each point.
3Join with a ruler.

Draw the graph of y = 2x + 3.

x12342x2468y123451234567891011120xy57911
(1, 5)(2, 7)(3, 9)(4, 11)

Draw the graph of y = 2x + 2.

x12342xy123451234567891011120xy246846810
1Work out each y.
2Plot each point.
3Join with a ruler.
(1, 4)(2, 6)(3, 8)(4, 10)
1Work out each y.
2Plot each point.
3Join with a ruler.

Draw the graph of y = 3x + 2.

x1233xy123451234567891011120xy3695811
(1, 5)(2, 8)(3, 11)

Copy and complete each table.

1

y = 2x + 7

x012
2x024
y7911
2

y = 3x + 3

x012
3x036
y369
3

y = 2x + 1

x1234
2x2468
y3579
1Work out each y.
2Plot each point.
3Join with a ruler.

Thumbs up for yes. Thumbs down for no.

  1. Is (2, 5) on the line y = 2x + 1?

    Yes

  2. Is (3, 7) on the line y = x + 3?

    No: when x = 3, y = 6

  3. Is (1, 5) on the line y = 3x + 2?

    Yes

  4. Is (4, 9) on the line y = 2x + 1?

    Yes

  5. Is (0, 4) on the line y = 2x?

    No: when x = 0, y = 0

Plotting straight-line graphs worksheet, page 1

Plotting straight-line graphs worksheet, page 2

Answer sheet

  1. y = x + 3. Work out y when x = −2.

    y = 1

  2. The point (2, k) is on the line y = 3x + 1. What is k?

    k = 7

  3. The points (0, 1), (1, 3), (2, 5) are on a line. Which rule is it: y = x + 1 or y = 2x + 1?

    y = 2x + 1

  4. Does the line y = 10 − x go up or down? How do you know?

    Down: y gets smaller

  1. Here is the table for y = 2x. Plot each point. Join them with a ruler.

    line through (0, 0) and (3, 6)
    x0123y0246

  2. Complete the table for y = 2x + 5.

    7, 9, 11
    x1232xy

  3. Draw the graph of y = x + 3 on the grid in question 1.

    line through (0, 3) and (3, 6)
Exit tickets to print