1. 17/01/2019
Straight lines

2. 17/01/2019
y = mx + c
All straight line graphs follow the general equation
y = mx + c
For example:
y = 5x + 1
y = 3x - 2

3. PLOTTING STRAIGHT LINE GRAPHS
17/01/2019
PLOTTING STRAIGHT LINE GRAPHS

4. 17/01/2019 x 1 2 3 4 5 y Example: Draw the graph of y = x + 2
Step 1: We start by drawing a table of values for the graph we are trying to draw... x 1 2 3 4 5 y

5. 17/01/2019
Co-ordinates
(2, 3)
Along the corridor
Up the stairs

6. 17/01/2019

7. 17/01/2019 Example: Draw the graph of y = x + 2
Step 2: We use our table of coordinates to plot each point on a set of axes...
Step 3: Join these points to form a straight line x 1 2 3 4 5 y 6 7 1 2 3 4 5 6

8. 17/01/2019
Task – Draw the graphs of the following equations on a +10 to -10 axis. Start by copying and completing these tables x 1 2 3 4 5 y
1) y = x + 4 x 1 2 3 4 5 y
y = x – 1 x 1 2 3 4 5 y
3) y = 2x+3 x 1 2 3 4 5 y
4) y = 3x-1

9. 17/01/2019
Other special lines

10. 17/01/2019
On a spare grid can you
Draw the following lines?
X = 2
X=-3
X=1
X = -5

11. 17/01/2019
On a second one can you
Draw the following lines?
y = 4
Y =-5
Y =2
y = -3

12. 17/01/2019
𝒚=𝒎𝒙+𝒄

13. 17/01/2019
𝑦 = m𝑥 + c
All straight lines have equations which can be written in the form
m is the GRADIENT (for each 1 unit right, how many units up?)
c is the 𝒚-INTERCEPT (where does the graph cut the 𝒚-axis?)

14. ‘For every one to the right I go up m’
17/01/2019
Gradient
Gradient means steepness of the slope
‘For every one to the right I go up m’
The gradient, m, is always the coefficient of 𝒙 (the number attached to the 𝑥 in the equation)
𝑦 = 3𝑥 + 2 gradient is 3
So for every 1 across to the right, I go UP 3
𝑦 = -4𝑥 - 1 gradient is -4
So for every 1 across to the right, I go DOWN 4
𝑦 = 2 + 7𝑥 gradient is 7
So for every 1 across to the right, I go UP 7

15. ‘Where does the graph meet or cross the y-axis?’
17/01/2019
𝑦-intercept
Intercept sounds like intersect, which means meet or cross
‘Where does the graph meet or cross the y-axis?’
The 𝑦-intercept is the number with no letter attached to it
𝑦 = 3𝑥 + 2 intercept is at 2
So the graph crosses y axis at 2
𝑦 = -4𝑥 - 1 intercept is at -1
So the graph crosses y axis at 4
𝑦 = 2 + 7𝑥 intercept is at 2
So the graph crosses y axis at 2

16. On your mini whiteboards… Quick Questions!
17/01/2019
𝒚 = m𝒙 + c
On your mini whiteboards… Quick Questions!

17. 17/01/2019
What is the GRADIENT of
𝑦 = 2𝑥 + 3

18. 17/01/2019
What is the GRADIENT of
𝑦 = 5𝑥 – 3

19. 17/01/2019
What is the GRADIENT of
𝑦 = -5𝑥 – 3

20. 17/01/2019
What is the GRADIENT of
𝑦 = 100𝑥 – 3

21. 17/01/2019
Which is STEEPER?
𝑦 = 3𝑥 or 𝑦 = 8𝑥 + 6

22. 17/01/2019
Which is STEEPER?
𝑦 = -3𝑥 or 𝑦 = -8𝑥 + 6

23. 17/01/2019
Sketching graphs

24. 𝑦 = 3𝑥 + 2 gradient 3 3 𝑦-intercept (0,2) 17/01/2019 Example (0,2)

25. 𝑦 = -2𝑥 + 1 gradient -2 𝑦-intercept (0,1) -2 17/01/2019 Example (0,1)

26. 17/01/2019
Task – Draw the following graphs on your grids using the gradient/intercept method
1) y = 2x ) y = 3x – 2 3) y = 2x – 1
y = x ) y = x – 3 6) y = 3x + 1
y = - 2x ) y = 3 – x 9) y = -3x – 1
y = 1 2 x ) y = 1 3 x – 2 12) y = 1 4 x
y = 2 3 x ) y = 2 – 1 2 x 15) y = -x

27. 17/01/2019
Solutions - Green

28. 17/01/2019
Solutions - Orange

29. On your mini whiteboards… Quick Questions!
17/01/2019
𝒚 = m𝒙 + c
On your mini whiteboards… Quick Questions!

30. Which line(s) has a y intercept of 4?
17/01/2019
Which line(s) has a y intercept of 4? 3 2 -4 4 -1 1 -3 -2

31. Which line(s) has a gradient of 2?
17/01/2019
Which line(s) has a gradient of 2? 3 2 -4 4 -1 1 -3 -2

32. What are the equations of these lines:
17/01/2019
Summary of skills
What are the equations of these lines:
Line 1
Line 2
Line 3

33. PLOTTING QUADRATICS (Double brackets)
17/01/2019
PLOTTING QUADRATICS (Double brackets)

34. 17/01/2019
Quadratic graphs
Quadratic equations…
𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐
…have graphs of a certain shape which we call a parabola
If 𝑎 is positive, then the shape will be a “u”
If 𝑎 is negative, then the shape will be an “n”
To plot
Substitute values of 𝑥 into the equation to find the corresponding 𝑦 values
Plot points and join with a smooth curve

35. 17/01/2019 Examples Here are examples of three quadratic functions:
y = x2
y = x2 – 3x
y = –3x2

36. 17/01/2019 Example Plot the graph of y = x2 – 3
for values of x between –3 and 3.
We can use a table of values to generate coordinates that lie on the graph as follows: x
y = x2 – 3 –3 –2 –1 1 2 3 6 1 –2 –3 –2 1 6
(–3, 6)
(–2, 1)
(–1, –2)
(0, –3)
(1, –2)
(2, 1)
(3, 6)

37. 17/01/2019 Example x y = x2 – 3 –3 –2 –1 1 2 3 6 1 –2 –3 –2 1 61 2 3 6 1 –2 –3 –2 1 6
The points given in the table are plotted … x –2 –1 –3 1 2 3 4 5 y
… and the points are then joined together with a smooth curve.
The shape of this graph is called a parabola.
It is characteristic of a quadratic function.

38. 17/01/2019
Task – For each equation, make a table of values, draw the axes and plot the graph
1) y = x { - 7 < x < 7 }
Ans
6) y = x { - 5 < x < 7 }
Ans
2) y = 2x { - 4 < x < 4 }
Ans
7) y = x2 + 2x {- 5 < x < 5 }
Ans
3) y = 3x { - 4 < x < 4 }
Ans
8) y = x2 - 3x {- 5 < x < 5 }
Ans
4) y = ½x { - 6 < x < 6 }
Ans
9) y = x2 + 3x {- 5 < x < 5 }
Ans
5) y = x { - 6 < x < 6 }
Ans
10) y = x2 - 4x {- 5 < x < 7 }
Ans

39. x
- 7
- 6
- 5
- 4
- 3
- 2
- 1 1 2 3 4 5 6 7 y 9 16 25 36 49 49 36 25 16 9 4 1 y 50 x x
y = x2 40 x x 30 x x 20 x x 10 x x x x x x x x
Back to questions

40. x
- 5
- 4
- 3
- 2
- 1 1 2 3 4 5 y 50 32 18 8 y 50 x x
y = 2x2 40 x x 30 20 x x 10 x x x x x x
Back to questions

41. x
- 4
- 3
- 2
- 1 1 2 3 4 y 48 27 12 y 50 x x 40
y = 3x2 30 x x 20 x x 10 x x x x
Back to questions

42. x
- 6
- 5
- 4
- 3
- 2
- 1 1 2 3 4 5 6 y 18
12.5 8
4.5
0.5 y x 18 16 14 12 10 8 6 4 2 -2 x
y = ½x2 x x x x x x x x x x x x
Back to questions

43. x
- 6
- 5
- 4
- 3
- 2
- 1 1 2 3 4 5 6 y 41 30 21 14 9 y 50 x 40 x
y = x2 + 5 x 30 x x 20 x x x 10 x x x x x x
Back to questions

44. x
- 5
- 4
- 3
- 2
- 1 1 2 3 4 5 6 7 y
- 11
- 16
- 19
- 20 16 29 y 30 25 20 15 10 5 -5
-10
-15
-20 x
y = x2 - 20 x x x x x x x x x x x x x
Back to questions

45. x
- 5
- 4
- 3
- 2
- 1 1 2 3 4 5 y 15 8 24 35 y 50 40 x 30
y = x2 + 2x x 20 x x 10 x x x x x x x x
Back to questions

46. x
- 5
- 4
- 3
- 2
- 1 1 2 3 4 5 y 40 28 18 10 y 50 40 x 30
y = x2 – 3x x 20 x x 10 x x x x x x x x
Back to questions

47. x
- 5
- 4
- 3
- 2
- 1 1 2 3 4 5 y 20 14 10 8 28 38 50 y 50 x 40 x
y = x2 + 3x + 10 30 x 20 x x x x 10 x x x x x
Back to questions

48. x
- 5
- 4
- 3
- 2
- 1 1 2 3 4 5 6 7 y 35 22 11
- 10
- 13
- 14 y x 35 30 25 20 15 10 5
y = x2 - 4x - 10 x x x x x x x -5
-10
-15
-20 x x x x x x
Back to questions