1. Linear Graphs – Tables of Values Method – Complete Lesson
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2. Starter
A task at the beginning of the lesson that reviews a skill required for the learning.
Knowledge Check
Questions to assess students’ current understanding and to consequently show progress.
Real-Life Example
A ‘hook’ to raise interest and provide a concrete example.
Demonstration
Slides for a teacher to lead students – didactically or via questioning – through a mathematical method.
AFL Questions
Assessment For Learning Questions, used to assess students’ competency for independent tasks/activities.
Plenary
An opportunity for students to prove/evaluate their learning.

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6. STARTER Coordinates What are the coordinates of the….
… circle? (____ , _____)
… star? (____ , _____)
… rectangle?
… square?
… hexagon?
… equilateral triangle?
… pentagon?
… isosceles triangle?
… trapezium?
… octagon?
Plot (mark) coordinates (2 , 5) & (−5 , −2)
Join the two points with a line.
Plot (mark) coordinates (6 , −5) & (−7 , 8)
Join the two points with a line.
What can we say about where
these lines cross?

7. STARTER (7 , 8) (4 , 5) (0 , 7) (8 , 0) (− 4 , 3) (− 9 , 0) (5 , − 8)
Coordinates
What are the coordinates of the….
(7 , 8)
… circle? (____ , _____)
… star? (____ , _____)
… rectangle?
… square?
… hexagon?
… equilateral triangle?
… pentagon?
… isosceles triangle?
… trapezium?
… octagon?
(4 , 5)
(0 , 7)
(8 , 0)
(− 4 , 3)
(− 9 , 0)
(5 , − 8)
(2 , − 4)
(0 , − 7)
(− 6 , −3)
Plot (mark) coordinates (2 , 5) & (−5 , −2)
Join the two points with a line.
Plot (mark) coordinates (6 , −5) & (−7 , 8)
Join the two points with a line.
They are at 90°
(perpendicular).
What can we say about where
these lines cross?

9. Two-Step Function Machines
STARTER
× 3
− 4
Two-Step Function Machines
INPUT 2 4 −1 −2
OUTPUT 2 8 −4 −7
−10
Calculate the output for each input.
INPUT
Double
Add 3
OUTPUT
INPUT 1 2 4 −2
OUTPUT 5
÷ 2
+ 2
INPUT 6
OUTPUT 2 1

10. Two-Step Function Machines
STARTER
× 3
− 4
Two-Step Function Machines
INPUT 2 4 −1 −2
OUTPUT 2 8 −4 −7
−10
Calculate the output for each input.
INPUT
Double
Add 3
OUTPUT
INPUT 1 2 4 −2
OUTPUT 5 7 11 3 −1
÷ 2
+ 2
INPUT 6 −2 −4
OUTPUT 5 2 1
Answers

11. LOPT
PLOT
INEL
LINE
RGHAP
GRAPH
ATRDENCOOI
COORDINATE
UQIENAOT
EQUATION
EILANR
LINEAR

12. Plotting Linear Graphs:
20 August 2019
Plotting Linear Graphs:
Table of Values

13. 𝑦=𝑥+3 𝑦=2𝑥−1 𝑦= 1 2 𝑥−1 𝑦=1−3𝑥 Plot one of these lines KNOWLEDGE CHECK
using a table of values.
KNOWLEDGE CHECK
𝑦=𝑥+3
𝑦=2𝑥−1
𝑦= 1 2 𝑥−1
Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson.
𝑦=1−3𝑥

14. 𝑦=𝑥+3 𝑦=2𝑥−1 𝑦= 1 2 𝑥−1 𝑦=1−3𝑥 Plot one of these lines KNOWLEDGE CHECK
using a table of values.
KNOWLEDGE CHECK
𝑦=𝑥+3
𝑦=2𝑥−1
𝑦= 1 2 𝑥−1
Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson.
𝑦=1−3𝑥

15. + 3 × 2 𝑥 𝑦 𝑦=2𝑥+3 $7 $9 $23 𝑥=𝑀𝑖𝑙𝑒𝑠 𝑦=𝐶𝑜𝑠𝑡
A taxi charges $2 per mile.
There is also a $3 callout charge.
How much does it cost to go…
2 miles?
3 miles?
10 miles? $7 $9
$23 $
Miles 𝑥 𝑦
How is distance related to cost?
Can you draw a function machine?
Can you write an equation?
+ 3
× 2 𝑥 𝑦
𝑥=𝑀𝑖𝑙𝑒𝑠
𝑦=𝐶𝑜𝑠𝑡
𝑦=2𝑥+3

16. 𝑦=2𝑥+3 Vocabulary 𝑦-axis Equation 𝑥, 𝑦 values Point 𝑥-axis Variables
We plot, or draw,
a graph on a grid.
The line represents all
the values where the
equation is true, is satisfied.
Origin
(0 , 0)
Line Segment
(it goes forever)

17. 𝑦=2𝑥+3 One method to draw a straight line is to substitute values
for 𝑥 and 𝑦 into the equation.
To make it easy,
we use a table of values.

18. + 2 𝑥 𝑦 𝑦=𝑥+2 × × × × × × × 𝑦=𝑥+2 𝑥 −3 −2 −1 1 2 3 𝑦 4 5
Draw the graph of:
Always label your line!
𝑦=𝑥+2
𝑦=𝑥+2
1) Express the equation as
a function machine. × ×
+ 2 𝑥 𝑦 × × ×
2) Complete a Table of Values. × × 𝑥 −3 −2 −1 1 2 3 𝑦 4 5
3) Plot each pair of values as coordinates.
4) Join the points to make a line.

19. − 3 𝑥 𝑦 𝑦=𝑥−3 × × × × × × × 𝑥 −3 −2 −1 1 2 3 𝑦 −6 −5 −4 𝑦=𝑥−3
Draw the graph of:
𝑦=𝑥−3
1) Express the equation as
a function machine.
− 3 𝑥 𝑦
2) Complete a Table of Values. × × 𝑥 −3 −2 −1 1 2 3 𝑦 −6 −5 −4 × × × × ×
3) Plot each pair of values as coordinates.
𝑦=𝑥−3
4) Join the points to make a line.

20. × 2 𝑥 𝑦 𝑦=2𝑥 × × × × × × × 𝑦=2𝑥 𝑥 −3 −2 −1 1 2 3 𝑦 −6 −4 4 6
Draw the graph of:
𝑦=2𝑥
𝑦=2𝑥 ×
1) Express the equation as
a function machine. ×
× 2 𝑥 𝑦 ×
2) Complete a Table of Values. × 𝑥 −3 −2 −1 1 2 3 𝑦 −6 −4 4 6 × × ×
3) Plot each pair of values as coordinates.
4) Join the points to make a line.

21. + 1 × 2 𝑥 𝑦 𝑦=2𝑥+1 × × × × × × ?? 𝑦=2𝑥+1 𝑥 −3 −2 −1 1 2 3 𝑦 −5 5 7
Draw the graph of:
𝑦=2𝑥+1
𝑦=2𝑥+1
1) Express the equation as
a function machine. ×
+ 1
× 2 𝑥 𝑦 × ×
2) Complete a Table of Values. × 𝑥 −3 −2 −1 1 2 3 𝑦 −5 5 7 × ?? ×
3) Plot each pair of values as coordinates.
4) Join the points to make a line.

22. − 4 × 3 𝑥 𝑦 𝑦=3𝑥−4 × × × × 𝑦=3𝑥−4 𝑥 −3 −2 −1 1 2 3 𝑦 −13 −12 −7 −4 5
Draw the graph of:
𝑦=3𝑥−4
𝑦=3𝑥−4
1) Express the equation as
a function machine. ×
− 4
× 3 𝑥 𝑦 ×
2) Complete a Table of Values. × 𝑥 −3 −2 −1 1 2 3 𝑦
−13
−12 −7 −4 5 ×
3) Plot each pair of values as coordinates.
4) Join the points to make a line.

23. 𝑦=𝑥+4 𝑦=𝑥+4 𝑥 −3 −2 −1 1 2 3 𝑦 4 5 6 7 Draw the graph of:
1) Complete a Table of Values. 𝑥 −3 −2 −1 1 2 3 𝑦 4 5 6 7
2) Plot each pair of values as coordinates.
3) Join the points to make a line.

24. 𝑦=2𝑥+1 𝑦=2𝑥+1 𝑥 −3 −2 −1 1 2 3 𝑦 −5 5 7 Draw the graph of:
1) Complete a Table of Values. 𝑥 −3 −2 −1 1 2 3 𝑦 −5 5 7
2) Plot each pair of values as coordinates.
3) Join the points to make a line.

25. Draw the graph of:
𝑦= 1 2 𝑥+2
𝑦= 1 2 𝑥+2
1) Complete a Table of Values. 𝑥 −3 −2 −1 1 2 3 𝑦
0.5
1.5
2.5
3.5
2) Plot each pair of values as coordinates.
3) Join the points to make a line.

26. 𝑦=2−2𝑥 𝑦=2−2𝑥 𝑥 −3 −2 −1 1 2 3 𝑦 8 6 4 −4 Draw the graph of:
1) Complete a Table of Values. 𝑥 −3 −2 −1 1 2 3 𝑦 8 6 4 −4
2) Plot each pair of values as coordinates.
3) Join the points to make a line.

27. 𝑦=2𝑥+3 𝑥 −2 𝑦 3 −1 You only need 2 points to plot a straight line.
Why bother with the rest?
Do you agree?
𝑦=2𝑥+3
𝑦=2𝑥+3 𝑥 −2 𝑦 3 −1

28. 𝑦=𝑥+3 𝑦=2𝑥 𝑦=3𝑥−4 𝑦=3−2𝑥 𝑥 −3 −2 −1 1 2 3 𝑦 4 𝑥 −3 −2 −1 1 2 3 𝑦 6 𝑥
Complete a table of values for each equation.
Can you spot some mistakes?
𝑦=𝑥+3
𝑦=2𝑥 𝑥 −3 −2 −1 1 2 3 𝑦 4 𝑥 −3 −2 −1 1 2 3 𝑦 6
𝑦=3𝑥−4
𝑦=3−2𝑥 𝑥 −3 −2 −1 1 2 3 𝑦
−13 𝑥 −3 −2 −1 1 2 3 𝑦 7 6

29. Are there patterns in the values?
𝑦=𝑥+3
𝑦=2𝑥 𝑥 −3 −2 −1 1 2 3 𝑦 4 5 6 𝑥 −3 −2 −1 1 2 3 𝑦 −6 4 6 3 −4
𝑦=3𝑥−4
𝑦=3−2𝑥 𝑥 −3 −2 −1 1 2 3 𝑦
−13
−10 −7 −4 5 𝑥 −3 −2 −1 1 2 3 𝑦 9 7 6 2 5

30. 𝑦=2𝑥+1 𝑦=3𝑥−5 𝑦= 1 2 𝑥+2 𝑦+2𝑥=2 𝑥 −3 −2 −1 1 2 3 𝑦 𝑥 −3 −2 −1 1 2 3 𝑦
Complete a table of values for each equation.
Can you spot some mistakes?
𝑦=2𝑥+1
𝑦=3𝑥−5 𝑥 −3 −2 −1 1 2 3 𝑦 𝑥 −3 −2 −1 1 2 3 𝑦
−14
𝑦= 1 2 𝑥+2
𝑦+2𝑥=2 𝑥 −3 −2 −1 1 2 3 𝑦
1.5
3.5 𝑥 −3 −2 −1 1 2 3 𝑦 7 −4

31. Are there patterns in the values?
𝑦=2𝑥+1
𝑦=3𝑥−5 𝑥 −3 −2 −1 1 2 3 𝑦 −5 5 7 𝑥 −3 −2 −1 1 2 3 𝑦
−14
−11 −8 −5 4 −3 1
𝑦= 1 2 𝑥+2
𝑦+2𝑥=2 𝑥 −3 −2 −1 1 2 3 𝑦
1.5
2.5
3.5 𝑥 −3 −2 −1 1 2 3 𝑦 7 6 4 −4
0.5 8

32. You will need to make your own
Drawing Straight Line Graphs ①
1) Draw the graph of 𝑦 =𝑥+2
a) Complete the table of values
for each value of 𝑥 𝒙 −3 −2 −1 1 2 3 𝒚 4
b) Plot each pair of 𝑥 and 𝑦 values.
c) Join the points into a line and label. 𝒙 −3 −2 −1 1 2 3 𝒚
2) On the same grid,
draw the graph of 𝑦 =𝑥−2 𝒙 −3 −2 −1 1 2 3 𝒚
3) On the same grid,
draw the graph of 𝑦 =𝑥+4
4) What can we say about these 3 lines?
5) On the grid,
draw the graph of 𝑦 =2𝑥+1
You will need to make your own
table of values below.

33. You will need to make your own
Drawing Straight Line Graphs ①
𝑦 =𝑥+4
1) Draw the graph of 𝑦 =𝑥+2
𝑦 =𝑥+2
a) Complete the table of values
for each value of 𝑥 𝒙 −3 −2 −1 1 2 3 𝒚 4 5
b) Plot each pair of 𝑥 and 𝑦 values.
c) Join the points into a line and label.
𝑦 =𝑥−2 𝒙 −3 −2 −1 1 2 3 𝒚 −5 −4
2) On the same grid,
draw the graph of 𝑦 =𝑥−2 𝒙 −3 −2 −1 1 2 3 𝒚 4 5 6 7
3) On the same grid,
draw the graph of 𝑦 =𝑥+4
4) What can we say about these 3 lines?
They are parallel
5) On the grid,
draw the graph of 𝑦 =2𝑥+1
You will need to make your own
table of values below.
𝑦 =2𝑥+1 𝒙 −3 −2 −1 1 2 3 𝒚 −5 5 7

34. Drawing Straight Line Graphs①
Drawing Straight Line Graphs ①
1) Draw the graph of 𝑦 =𝑥+2
1) Draw the graph of 𝑦 =𝑥+2
a) Complete the table of values
for each value of 𝑥
a) Complete the table of values
for each value of 𝑥 𝒙 −3 −2 −1 1 2 3 𝒚 4 𝒙 −3 −2 −1 1 2 3 𝒚 4
b) Plot each pair of 𝑥 and 𝑦 values.
b) Plot each pair of 𝑥 and 𝑦 values.
c) Join the points into a line and label.
c) Join the points into a line and label. 𝒙 −3 −2 −1 1 2 3 𝒚 𝒙 −3 −2 −1 1 2 3 𝒚
2) On the same grid,
draw the graph of 𝑦 =𝑥−2
2) On the same grid,
draw the graph of 𝑦 =𝑥−2 𝒙 −3 −2 −1 1 2 3 𝒚 𝒙 −3 −2 −1 1 2 3 𝒚
3) On the same grid,
draw the graph of 𝑦 =𝑥+4
3) On the same grid,
draw the graph of 𝑦 =𝑥+4
4) What can we say about these 3 lines?
4) What can we say about these 3 lines?
5) On the grid,
draw the graph of 𝑦 =2𝑥+1
You will need to make your own
table of values below.
5) On the grid,
draw the graph of 𝑦 =2𝑥+1
You will need to make your own
table of values below.

36. ② −3 −2 −1 1 2 3 A: 𝑦 =3𝑥−2 B: 𝑦 = 1 2 𝑥−2 C: 𝑦 =3𝑥+3
Drawing Straight Line Graphs ②
1) Draw the graph of 𝑦 =𝑥+1
a) Complete the table of values
for each value of 𝑥 𝒙 −3 −2 −1 1 2 3 𝒚
b) Plot each pair of 𝑥 and 𝑦 values.
c) Join the points into a line and label.
2) On the same grid,
draw the graph of 𝑦 =2𝑥+1
Use your own table of values.
3) What can we say about these 2 lines?
4) Draw the graphs of…
A: 𝑦 =3𝑥−2
B: 𝑦 = 1 2 𝑥−2
C: 𝑦 =3𝑥+3
5) What links A & B?
6) What links A & C?

37. C A B ② They cross the 𝑦-axis at the same point.
Drawing Straight Line Graphs ②
1) Draw the graph of 𝑦 =𝑥+1
a) Complete the table of values
for each value of 𝑥 𝒙 −3 −2 −1 1 2 3 𝒚 4
𝑦 =𝑥+1
b) Plot each pair of 𝑥 and 𝑦 values.
c) Join the points into a line and label.
2) On the same grid,
draw the graph of 𝑦 =2𝑥+1
Use your own table of values.
𝑦 =2𝑥+1
3) What can we say about these 2 lines?
They cross the 𝑦-axis at the same point.
4) Draw the graphs of… C A
A: 𝑦 =3𝑥−2
B: 𝑦 = 1 2 𝑥−2 B
C: 𝑦 =3𝑥+3
5) What links A & B?
They cross the 𝑦-axis at the same point.
6) What links A & C?
They have the same gradient.

38. ② ② −3 −2 −1 1 2 3 −3 −2 −1 1 2 3 A: 𝑦 =3𝑥−2 A: 𝑦 =3𝑥−2 B: 𝑦 = 1 2 𝑥−2
Drawing Straight Line Graphs ②
Drawing Straight Line Graphs ②
1) Draw the graph of 𝑦 =𝑥+1
1) Draw the graph of 𝑦 =𝑥+1
a) Complete the table of values
for each value of 𝑥
a) Complete the table of values
for each value of 𝑥 𝒙 −3 −2 −1 1 2 3 𝒚 𝒙 −3 −2 −1 1 2 3 𝒚
b) Plot each pair of 𝑥 and 𝑦 values.
b) Plot each pair of 𝑥 and 𝑦 values.
c) Join the points into a line and label.
c) Join the points into a line and label.
2) On the same grid,
draw the graph of 𝑦 =2𝑥+1
Use your own table of values.
2) On the same grid,
draw the graph of 𝑦 =2𝑥+1
Use your own table of values.
3) What can we say about these 2 lines?
3) What can we say about these 2 lines?
4) Draw the graphs of…
4) Draw the graphs of…
A: 𝑦 =3𝑥−2
A: 𝑦 =3𝑥−2
B: 𝑦 = 1 2 𝑥−2
B: 𝑦 = 1 2 𝑥−2
C: 𝑦 =3𝑥+3
C: 𝑦 =3𝑥+3
5) What links A & B?
5) What links A & B?
6) What links A & C?
6) What links A & C?

40. ③ −3 −2 −1 1 2 3 A: 𝑦 = 1 4 𝑥+1 B: 𝑦 =3−4𝑥 C: 𝑦+4𝑥=−5
Drawing Straight Line Graphs ③
1) Draw the graph of 𝑦 =2𝑥+3 𝒙 −3 −2 −1 1 2 3 𝒚
2) On the same grid,
draw the graph of 𝑦 = 1 2 𝑥+3
Use your own table of values.
3) What do these lines share?
1) Draw the graphs.
Choose values for 𝑥 to make the table of values easy to complete.
A: 𝑦 = 1 4 𝑥+1
B: 𝑦 =3−4𝑥
C: 𝑦+4𝑥=−5
5) What links A & B?
6) What links B & C?

41. They cross the 𝑦-axis at the same point.
Drawing Straight Line Graphs ③
1) Draw the graph of 𝑦 =2𝑥+3 𝒙 −3 −2 −1 1 2 3 𝒚 5 7 9
𝑦 = 1 2 𝑥+3
2) On the same grid,
draw the graph of 𝑦 = 1 2 𝑥+3
Use your own table of values.
𝑦 =2𝑥+3
3) What do these lines share?
They cross the 𝑦-axis at the same point.
1) Draw the graphs.
Choose values for 𝑥 to make the table of values easy to complete.
𝑦 =3−4𝑥
A: 𝑦 = 1 4 𝑥+1
𝑦+4𝑥=−5
𝑦 = 1 4 𝑥+1
B: 𝑦 =3−4𝑥
C: 𝑦+4𝑥=−5
5) What links A & B?
Cross at 90°
6) What links B & C?
Parallel

42. ③ ③ −3 −2 −1 1 2 3 −3 −2 −1 1 2 3 A: 𝑦 = 1 4 𝑥+1 A: 𝑦 = 1 4 𝑥+1
Drawing Straight Line Graphs ③
Drawing Straight Line Graphs ③
1) Draw the graph of 𝑦 =2𝑥+3
1) Draw the graph of 𝑦 =2𝑥+3 𝒙 −3 −2 −1 1 2 3 𝒚 𝒙 −3 −2 −1 1 2 3 𝒚
2) On the same grid,
draw the graph of 𝑦 = 1 2 𝑥+3
Use your own table of values.
2) On the same grid,
draw the graph of 𝑦 = 1 2 𝑥+3
Use your own table of values.
3) What do these lines share?
3) What do these lines share?
1) Draw the graphs.
Choose values for 𝑥 to make the table of values easy to complete.
1) Draw the graphs.
Choose values for 𝑥 to make the table of values easy to complete.
A: 𝑦 = 1 4 𝑥+1
A: 𝑦 = 1 4 𝑥+1
B: 𝑦 =3−4𝑥
B: 𝑦 =3−4𝑥
C: 𝑦+4𝑥=−5
C: 𝑦+4𝑥=−5
5) What links A & B?
5) What links A & B?
6) What links B & C?
6) What links B & C?

44. 𝑦=𝑥+3 𝑦=2𝑥−1 𝑦= 1 2 𝑥−1 𝑦=1−3𝑥 Plot one of these lines KNOWLEDGE CHECK
using a table of values.
KNOWLEDGE CHECK
𝑦=𝑥+3
𝑦=2𝑥−1
𝑦= 1 2 𝑥−1
Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson.
𝑦=1−3𝑥

45. 𝑦=𝑥+3 𝑦=2𝑥−1 𝑦= 1 2 𝑥−1 𝑦=1−3𝑥 Plot one of these lines KNOWLEDGE CHECK
using a table of values.
KNOWLEDGE CHECK
𝑦=𝑥+3
𝑦=2𝑥−1
𝑦= 1 2 𝑥−1
Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson.
𝑦=1−3𝑥

46. What do the three lines share on each grid? 𝑦= 1 2 𝑥+3 𝑦=2𝑥+3 𝑦=2𝑥+5
𝑦=2𝑥−4
𝑦=−𝑥+3
𝑦=2𝑥+3
What do the three lines
share on each grid?

47. Different lines, same 𝒚-intercept. What do the three lines
𝑦= 1 2 𝑥+3
Different lines,
same 𝒚-intercept.
𝑦=2𝑥+3
𝑦=2𝑥+5
𝑦=2𝑥−4
𝑦=−𝑥+3
𝑦=2𝑥+3
What do the three lines
share on each grid?
Different lines,
same gradient.

48. Can you calculate the equationsD A B
The green line is 𝑦=2𝑥+3
Can you calculate the equations
of the other lines?
The green line has…
…a gradient of 2.
…a 𝒚-intercept of 3.
A: 𝑦=2𝑥−1
B: 𝑦=2𝑥−6
C: 𝑦=𝑥+3
D: 𝑦=3−2𝑥 C

49. Check your success!
I can plot a straight line graph like 𝑦=𝑥+4 using a table of values.
I can plot straight line graphs like 𝑦=2𝑥−3 using a table of values.
I can plot straight line graphs and identify gradients and 𝑦-intercepts.

50. Check your success!
I can plot a straight line graph like 𝑦=𝑥+4 using a table of values.
I can plot straight line graphs like 𝑦=2𝑥−3 using a table of values.
I can plot straight line graphs and identify gradients and 𝑦-intercepts.

51. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to