1. Straight line graphs
A revision guide

2. Write down the co-ordinates of A, B, C and D :
(3,4) D
(-3,2) B
(1,-2) C
(-5,-3)

3. True or false?
Straight line equations can contain 𝒙 , 𝒙𝟐, 𝒐𝒓 𝒙𝟑 terms.
A True
B False
C Don’t know

4. Which one is the general equation of a straight line?
A 𝒙 = 𝒚𝒎 + 𝒄 B 𝒚 = 𝒎𝒙 +𝒄 C 𝒄 = 𝒎𝒚 + 𝒙

5. 𝒚=𝒎𝒙+𝒄 What does m represent in the equation of a straight line?
A the intercept
B the gradient
C the first coordinate

6. What does the gradient show?
A where the line hits the y-axis
B the steepness of the line
C where the line hits the x-axis

7. 𝒚=𝒎𝒙+𝒄 What does c represent in the equation of a straight line?
A the y-intercept
B the gradient
C the first coordinate

8. What does the y−intercept show?
A where the line hits the y-axis
B the steepness of the line
C where the line hits the x-axis

9. What is the gradient of the line 𝒚 = 𝟒𝒙 + 𝟐 ?
A The gradient is y
B The gradient is 2
C The gradient is 4

10. What is the y-intercept of the line 𝟐𝒚 =𝟒𝒙 −𝟔 ?
A The y-intercept is -6
B The y-intercept is 2
C The y-intercept is -3

11. The equation of the line with gradient = 1 and y-intercept = 5 is:
B 𝒚=𝟓𝒙+𝟏
C 𝒚=𝒙+𝟓

12. The equation of the line with a gradient = -1 and y-intercept = -4 is:
B 𝒚=−𝟒𝒙+𝟏
C 𝒚=− 𝒙−𝟒

13. The equation of the line with a gradient = 2 and y-intercept = -4 is:
B 𝒚=𝟐𝒙−𝟒
C 𝒚=−𝟒𝒙+𝟐

14. Summary 1 Co-ordinates are written as (x,y)
The general equation of a straight line is 𝒚=𝒎𝒙 + 𝒄
m is the gradient which describes the steepness of the line, the larger m is the steeper the line is!
c is the y-intercept, it is the point at which the line hits the y-axis
To identify the gradient and y-intercept of an equation, we must compare the equation to 𝒚=𝒎𝒙 + 𝒄
If the equation is NOT in the form 𝒚=𝒎𝒙 + 𝒄 then we must re-arrange the equation to get it in this form

15. What is the value of the y-intercept?
B 10
C 2

16. Which of these graphs has a negative gradient?
A line with a positive gradient goes up towards the POSITIVE QUADRANT
Which of these graphs has a negative gradient?
A Both graphs B Neither graph
C Graph A D Graph B

17. Which line has the largest Gradient?B
Steepness
If it were a SLIDE which one would scare you most ? C

18. Parallel lines have the same WHAT?
y-intercept
Gradient
x-intercept

19. Where (𝒙𝟏, 𝒚𝟏) and (𝒙𝟐, 𝒚𝟐) are co-ordinates on the line!
If you are given two co-ordinates, you can find the gradient of a straight line using the ‘formula’
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕= 𝑪𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒀 𝑪𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝑿
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕= 𝑪𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝑿 𝑪𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒀
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕= 𝑿 𝒀
𝒎= 𝒚𝟐−𝒚𝟏 𝒙𝟐−𝒙𝟏
Where (𝒙𝟏, 𝒚𝟏) and (𝒙𝟐, 𝒚𝟐) are co-ordinates on the line!

20. 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟏 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟐 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟎
Using 𝒎= 𝒚𝟐−𝒚𝟏 𝒙𝟐−𝒙𝟏 find the gradient of a line with co-ordinates (2,9) and (0,7)
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟏
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟐
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟎

21. 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕= 𝟏 𝟐 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟐 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=− 𝟏 𝟐
Using 𝒎= 𝒚𝟐−𝒚𝟏 𝒙𝟐−𝒙𝟏 find the gradient of a line with co-ordinates (3,3) and (-5,7)
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕= 𝟏 𝟐
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟐
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=− 𝟏 𝟐

22. 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟔 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=−𝟔 𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟑
Using 𝒎= 𝒚𝟐−𝒚𝟏 𝒙𝟐−𝒙𝟏 find the gradient of a line with co-ordinates (-5,3) and (-4,9)
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟔
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=−𝟔
𝑮𝒓𝒂𝒅𝒊𝒆𝒏𝒕=𝟑

23. Find any two co-ordinates which lie on the line with equation 𝒚 = 𝟐𝒙 − 𝟏

24. Are the points (0,-3) and (1,2) on the line with equation 𝒚 = 𝟔𝒙−𝟑 ?

25. Exercise 1: Write down the gradient and y-intercept of the lines with the following equations
𝑦=2𝑥−1
𝑦=5 − 1 2 𝑥
3𝑦=6𝑥+12 3
𝒚=𝟐𝒙+𝟒

26. 𝑦=𝑚𝑥+𝑐 a) m = 2 , c = 4 𝒚=𝟐𝒙+𝟒 b) m = -1 , c = -2 c) m = 1 , c = − 3 2
Exercise 2: Write down the equation of the line with the following gradients and y- intercepts
a) m = 2 , c = 4
b) m = -1 , c = -2
c) m = 1 , c = − 3 2
𝑦=𝑚𝑥+𝑐
𝒚=𝟐𝒙+𝟒
𝒚=−𝒙−𝟐
𝒚=𝒙− 𝟑 𝟐

27. 𝒎= 𝟑−𝟒 𝟒−𝟐 =− 𝟏 𝟐 𝒎= 𝟓−(−𝟓) 𝟓−𝟑 = 𝟏𝟎 𝟐 =𝟓 𝒎= 𝟐−(−𝟏) −𝟒−(−𝟑) = 𝟑 −𝟏 =−𝟑
Exercise 3: Using 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 find the gradient of the line with co-ordinates
(2,4) and (4,3)
(3,-5) and (5,5)
(-3,-1) and (-4,2)
𝒎= 𝟑−𝟒 𝟒−𝟐 =− 𝟏 𝟐
x1 , y1
x2 , y2
𝒎= 𝟓−(−𝟓) 𝟓−𝟑 = 𝟏𝟎 𝟐 =𝟓
x1 , y1
x2 , y2
𝒎= 𝟐−(−𝟏) −𝟒−(−𝟑) = 𝟑 −𝟏 =−𝟑
x1 , y1
x2 , y2

28. Exercise 4: Do these points lie on the line 𝒚=𝟑𝒙−𝟖?
(3,1)
x , y
𝒚=𝟑𝒙−𝟖
𝟏=𝟑(𝟑)−𝟖
𝟏=𝟗−𝟖
𝟏=𝟏
Equation is in BALANCE
SO THE POINT (3,1) LIES ON THE LINE!!!

29. Exercise 4: Do these points lie on the line 𝒚=𝟑𝒙−𝟖?
(2,4)
x , y
𝒚=𝟑𝒙−𝟖
𝟒=𝟑(𝟐)−𝟖
𝟒=𝟔−𝟖
𝟒=−𝟐
Equation is NOT in BALANCE
SO THE POINT (2,4) is NOT ON THE LINE!!!

30. Exercise 4: Do these points lie on the line 𝒚=𝟑𝒙−𝟖?
(0,-5)
x , y
𝒚=𝟑𝒙−𝟖
−𝟓=𝟑(𝟎)−𝟖
−𝟓=𝟎−𝟖
−𝟓=−𝟖
Equation is NOT in BALANCE
SO THE POINT (0,-5) is NOT ON THE LINE!!!

31. Exercise 5: Find any two co-ordinates on the following line 𝒚=𝟐𝒙+𝟑?
When 𝒙 = 𝟎
When 𝒙=𝟏
𝒚=𝟐𝒙+𝟑
(𝟎,𝟑)
𝒚=𝟐 𝟎 +𝟑
𝒚=𝟑
𝒚=𝟐𝒙+𝟑
(𝟏,𝟓)
𝒚=𝟐 𝟏 +𝟑
𝒚=𝟐+𝟑=𝟓

32. Exercise 6: Which of the following graphs are parallel?

33. Plotting a Graph: 𝒚=𝒙+𝟐 𝒙 -2 -1 1 2 𝒚 1 2 3 4 For the line 𝑦 = 𝑥 + 21 2 𝒚 1 2 3 4
For the line 𝑦 = 𝑥 + 2
when 𝒙 = −𝟐
𝑦 = −2 + 2
𝑦 = 0
when 𝒙 = −𝟏
𝑦 = −1 + 2
𝑦 = 1
when 𝒙 = 𝟎
𝑦 = 0 + 2
𝑦 = 2

34. Plotting Line Graphs 𝒙 -2 -1 1 2 𝒚
Co-ordinates 1 2 3 4
(-2, 0)
(-1, 1)
(0, 2)
(1, 3)
(2, 4)
Now we have some co-ordinates, so we just plot them to draw the line 

35. y y = x + 2 X X X X X X 5 4 3 2 x -2 -1 1 2 y Co-ordinates 1 2 3 4 11 2 y
Co-ordinates 1 2 3 4 X 1
(-2, 0)
(-1, 1)
(0, 2)
(1, 3)
(2, 4) X X -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5

36. HORIZONTAL & VERTICAL LINESy 1 -5 -4 -3 -2 -1 4 3 2 5
(x,y)
(3,4)
(3,1) x
y = -2
(-4,-2)
(0,-2)
(2,-2)
(3,-5)
x = 3

37. HORIZONTAL & VERTICAL LINESy 1 -5 -4 -3 -2 -1 4 3 2 5
(x,y)
(-2,4)
y = 2
(-4,2)
(0,2)
(2,2)
(-2,1) x
(-2,-5)
x = -2

38. HORIZONTAL & VERTICAL LINES
(x,y) y
x = 1
x = 5 4
x = -4 3 2
y = 1 1 1 x -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3
y = -4 4 -4 -5 5 2 3

39. 𝒚=𝟑𝒙−𝟐 TASK 1 A) Plot the straight line graph with equation
Take values of 𝑥 from -2 to 2
2cm ≡ 1 unit for the y-axis
4cm ≡ 1 unit for the x-axis
B) Write down the co-ordinate of the y-intercept
C) Draw the line 𝒚 = 𝟏 on the same axes
D) Write down the co-ordinate of their point of intersection

40. 𝒚=−𝒙+𝟒 TASK 2 A) Plot the straight line graph with equation
Take values of 𝑥 from -3 to 3
Use an appropriate scale
B) Write down the co-ordinate of the y-intercept
C) From the graph find the y when 𝒙 = −𝟏.𝟓
C) Draw the line 𝒙 =−𝟏 on the same axes
D) Write down the co-ordinate of the point of intersection of the two lines