1. Graphs of linear functions
Grade 4
Graphs of linear functions
Recognise, sketch and interpret graphs of linear functions
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Recognise, sketch and interpret graphs of linear functions
Grade 4
Prior Knowledge
Plotting linear graphs in the form y=mx + c
Drawing basic lines e.g. x=4, y=2, x=y
Rearranging equations
Duration
This is a 60 minutes learning episode. However, if knowledge and understanding of rearranging equations is weak then students will need additional time. It is advisable that this prior knowledge is secure before embarking on this topic as the exam questions almost always necessity this skill.
Resources
Print slides: 3, 9, 11, 16, 19
Equipment
Ruler
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Recapping key graph knowledge – plotting linear, drawing basic lines and recognising the form y=mx+c
Give students slide 3 printed. To work independently to complete (content should be recap of prior knowledge). Teacher circulation to check all are confident. Use slides 5, 6, 7 & 8 to review the answers collectively. Use this as an opportunity to use key vocabulary of gradient and y intercept. Also insist that students are drawing the lines using a ruler and a pencil. 20
Understand the gradient and y intercept (equation in the standard form of y = mx + c)
Give students slide 9 printed. Demo y = 4x + 1 using slide 10. Start first with the y intercept – plot this point and label. Then identify that the gradient is 4. This means move one step to the right and up (as positive) 4 steps. Students to complete 3 questions to check for understanding. 5
Rearranging equations into the form y= mx + c
Give students slide 11 printed (in colour as need to see the colour of the lines). Explain using 4x + 2y = 10 example on slide 12 that often the equations are not given in the standard y = mx + c form so we need to be confident in rearranging. Show the rearrangement and then plot. Continue to guide students in the 3 rearrangements (no graph sketching required). Students can then independently attempt the matching question which combines rearranging with linear function sketching. Extend to solving from the graph – show students slide 15.
Applying knowledge of y = mx + c in contextualised problems
Give students slide 16. Allow students to work on these independently initially before guiding them through each question using slide 17 and 18. For question 3 using the graph image to show how the 2.5 is the gradient of the line. 10
in an OCR exam question (from specimen papers)
Give students slide 19. This includes 2 exam questions related to objective. Relate to mark scheme to show how the marks are allocated.
Next Steps
Parallel, perpendicular lines, non linear equations
Assessment
PLC/Reformed Specification/Target 4/Algebra/Graphs Of Linear Functions

3. Graphs Recap Linear? y = 12-5x y = 3x + xˉ² y = 0.5x 4x + 3y = 6
Draw the lines:
x = 4, x = - 3
y = 5, y = -3
x = y
Draw the graph of y = 4x + 1 for values of x from -2 to 3
Linear?
y = 12-5x
y = 3x + xˉ²
y = x³ + 2x + 5
y = 0.5x
4x + 3y = 6
Rearrange y – 4x = 1 into the form y = mx + c
Rearrange y – 1 = 4x into the form y = mx + c
Student Sheet 1

4. Key Vocabulary
Graph Linear Function Y-intercept Power Gradient Point of intersection Variables

5. Graphs Recap Draw the graph of y = 4x + 1 for values of x from -2 to 2-1 1 2 y -7 -3 1 5 9

6. Graphs Recap Draw the lines: x = 4, x = - 3 y = 5, y = -3 x = y x = -3

7. Graphs Recap Rearrange y – 4x = 1 into the form y = mx + c y = 4x + 1+1 +1
y = 4x + 1
If you are given an equation of the line and it is not in the standard form y = mx + c you need to rearrange so that you can sketch easily.

8. How to recognise linear functions
Which of these are linear functions?
y = 12-5x
y = 3x + xˉ²
y = x³ + 2x + 5
y = 0.5x
4x + 3y = 6
By linear we mean that the function must create a straight line graph. The power of x must be 1
The power of x is 1
The power of x is 1 but also -2
The power of x is 1 but also 3
Linear equations are generally in the form y=mx + c
The power of x is 1
The power of x is 1

9. Sketching linear functions
DEMO
PRACTICE
Sketch the function y=4x+1 labelling the y-intercept.
Sketch the function y=2x- 3 labelling the y-intercept.
Sketch the function y=x-2 labelling the y-intercept.
Sketch the function y=3x+4 labelling the y-intercept.
Student Sheet 2

10. How to sketch linear functions
Sketch the function y=4x+1 labelling the y-intercept.
y=4x+1 is in the form y=mx+c
We now know that the y-intercept is 1 so the graph goes through the point (0,1).
As gradient=m=4, we can plot a second point on the line by going one step to the right and 4 steps up from (0,1).
With two known points on the line, we can sketch the line y=4x+1
y= 4x+1
(0,1)

11. Sketching linear functions – rearrange first
Practice Rearranging into the form y = mx + c
4x+2y=10
-2x = -y x – 3y = x + y = 4
Match each coloured line to its corresponding equation
A) y = -5x
B) x – y = 3
C) y = 2x + 1
D)y = 4x – 8
Student Sheet 3

12. Sketching linear functions – rearrange first
4x+2y=10
-4x
-4x
2y = -4x + 10
(0,5) ÷2 ÷2 ÷2
y = -4x + 5 2
y = -2x + 5
y intercept = 5
So point at (0,5)
Gradient -2
So one step to the left and DOWN 2 steps

13. Rearranging into the form y = mx + c
-2x = -y x + 3y = x + y = 4 +y +y -x -x
-4x
-4x
y – 2x = 7
y = -x + 4
3y = -4x + 18
+2x
+2x ÷3 ÷3 ÷3
y = 2x + 7
y = -4x + 6 3

14. Match each coloured line to its corresponding equation
A) y = -5x
B) x – y = 3
C) y = 2x + 1
D)y = 4x – 8
PURPLE
ORANGE
GREEN
BLACK

15. How to interpret linear functions
Sketch the graph 4x+2y=10. What does x equal when y=2?
(0,5)
Draw the line y=2 and read off the x-value and the point of intersection
x = 1.5

16. Problem Solving and Reasoning
Q1: The graph represents two cars, one blue and one red, coming to rest. (a) At what time was the blue car travelling at 10 m/s? b) What is the meaning of the y-intercept for the red car? c) What is the deceleration of the blue car? d) By observing the graph, which car decelerates the fastest and why?
Velocity (m/s)
Time (s)
Q2: Give a example of two variables with a linear relationship
Q3: Jack is tracking the growth of her plant. At present the plant has a height of 3cm. The plant grows at a rate of 2.5cm/day.
a) Create a linear model to represent the height of the plant after D days.
b) What will the plant’s height be after 24?
Student Sheet 4

17. Problem Solving and Reasoning
Q1: The graph represents two cars, one blue and one red, coming to rest. a) At what time was the blue car travelling at 10 m/s? 3s b) What is the meaning of the y-intercept for the red car? Initial velocity c) By observing the graph, which car decelerates the fastest and why? The blue car as it has a steeper gradient d) What is the deceleration of the blue car? Gradient=20/6=3.33 (3.s.f)
Velocity (m/s)
Time (s)

18. Reason and Explain
Q1: Give a example of two variables with a linear relationship Q2: Jack is tracking the growth of her plant. At present the plant has a height of 3cm. The plant grows at a rate of 2.5cm/day. a) Create a linear model to represent the height of the plant after D days. b) What will the plant’s height be after 24?
Miles and kilometres
Pounds and dollars
y = 2.5x + 3
y = 2.5 x
Height will be 63cm

19. Exam Questions – Specimen Papers
Student Sheet 5

20. Exam Questions – Specimen Papers

21. Exam Questions – Specimen Papers