Linear Graphs – Tables of Values Method – Complete Lesson Preview the presentation to check ability-level, AFL questions, and the animations during demonstrations. It is recommended to delete slides/sections not needed for your class.

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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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?

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?

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

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

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

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

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

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

+ 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

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)

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.

+ 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.

− 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.

× 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.

+ 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.

− 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.

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.

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.

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.

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.

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

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

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

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

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

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.

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

Drawing Straight Line Graphs ① 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.

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?

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.

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?

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?

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

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?

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

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

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?

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.

Can you calculate the equations D 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

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.

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.

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