1. Unit 4:Mathematics Aims Introduce linear equations. Objectives
Use algebra formula to plot straight line graphs.

2. y 4 3 2 1 -4 -3 -2 -1 x

3. Example 1 y 4 3 2 1 -4 -3 -2 -1 x
X = 3

4. Example 2 y 4 3 2 1 -4 -3 -2 -1
y = -1 x

5. Question 1 y 4 3 2 1 -4 -3 -2 -1 x

6. Question 2 y 4 3 2 1 -4 -3 -2 -1 x

7. Question 3 y 4 3 2 1 -4 -3 -2 -1 x

8. Question 4 y 4 3 2 1 -4 -3 -2 -1 x

9. Question 5 y 4 3 2 1 -4 -3 -2 -1 x

10. Question 6 y 4 3 2 1 -4 -3 -2 -1 x

11. Question 7 y 4 3 2 1 -4 -3 -2 -1 x

12. Straight-line graphs x -3 -2 -1 1 2 3 Y=x+3 4 5 x = -3 y = -3 + 3 = 0
Complete the table of values for y = x + 3, and then draw the graph from -3 to 3 for x
x = -3
y = = 0
x = -2,
y = = 1
x = 0
y = = 3
x = 3
y = = 6 x -3 -2 -1 1 2 3
Y=x+3 4 5

13. y 4 3 2 1 -4 -3 -2 -1 x

14. COORDINATE PLANE Y-axis X-axis Parts of a plane X-axis Y-axis Origin
Quadrants I-IV
Y-axis
QUAD II
QUAD I
Origin ( 0 , 0 )
X-axis
QUAD III
QUAD IV

15. PLOTTING POINTS
Remember when plotting points you always start at the origin. Next you go left or right. Then you go up or down. B C
Plot these 4 points
A (3, -4), B (5, 6), C (-4, 5) and D (-7, -5) A D

16. L SLOPE Run is 6 because we went to the right
Rise is 10 because we went up
Rise is -10 because we went down
Run is -6 because we went to the left

17. All straight lines can be written in the form y = mx + c
You need to be able to write down the equation of a straight line by working out the values for m and c.

18. c is the constant value – this part of the function does not change.
y = mx + c
m is the gradient of the line
This type of equation was made popular by the French Mathematician Rene Descartes.
“m” could stand for “Monter” – the French word meaning “to climb”.

19. y x Finding m and c y = mx +c 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6
It is very easy to find the value of c – this is the point at which the line crosses the y-axis.
Each time the lines moves 1 place to the right, it climbs up by 2 places.
So m = 2
Finding m is also easy in this case. The gradient means the rate at which the line is climbing.
y = mx +c
y = 2x +3

20. As the line travels across 1 position, it is not clear how far up it has moved.y x 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6
y = mx +c
But… any right angled triangle will give us the gradient! Let’s draw a larger one.
In general, to find the gradient of a straight line, we divide the…
vertical change by the…
horizontal change 2
y = mx +c
y = ½x - 2 4
The gradient, m = 2/4 = ½

21. Equation of a straight-line graph
The y-intercept of a graph is the y-coordinate of the point where the graph cuts the y-axis. It is usually denoted by c.

22. Equation of a straight-line graph.
Exercise.
Find the y-intercept of the following: 2)

23. Equation of a straight-line graph.
The gradient, steepness, of a line and its y-intercept define a line uniquely. In fact any straight line has an equation of the form: y = mx + c, where m is the gradient and c is the y-intercept. Example. Find the equation of the line with gradient 3 and y-intercept 4. Here m = 3 and c = 4. We substitute the values of m and c into the equation to obtain: y = 3x + 4.

24. Equation of a straight-line graph.
Exercise. Find the equations of the straight lines with the following gradients and y-intercepts: 1. Gradient of 4 and y-intercept of Gradient of –6 and y-intercept of 8 3. Gradient of ½ and y-intercept of –7.
(Answers: y = 4x + 2; y = -6x+8; y = ½ x - 7.)

25. Equation of a straight-line graph
We frequently need to find the equation of a line directly from its graph. We should:
Find the y-intercept, c.
Find the gradient, m, of the line.
Substitute these values into y = mx + c.
First, we find the y-intercept: c = 3.
Then we find the gradient: m =

26. Equation of a straight-line graph.
Example.
Find the equation of the line that goes through the points (2, 4) and (6, 12).
Choosing the point (6, 12) and substituting gives:
y = m χ x+ c
12 = 2 x 6 + c.
Rearranging gives: c = 0.
Hence y = 2x + 0
y = 2x.

27. FORMULA FOR FINDING SLOPE
Exercise. Find the equations of the lines that pass through the following points: 1. (0, 7) and (3, 13). 2. (2, 1) and (5, -1). 3. (4, 8) and (8, 0). 4. (-4, 2) and (12, 10).
1)Y=2x+7
2)y=-2 x + 7
3) y=-2x+16
4) y=1/2 x + 4