1. Session 10 – Straight Line Graphs
GCSE Maths

2. Coordinates
Graphs contain 2 axes, the horizontal one is called the x axis, the vertical is called the y axis
(x,y) like a claw-grab machine move horizontal then vertical
So the coordinate (3,2) is three horizontal then 2 vertical

3. The line y=x What are the coordinates of all the points on this line?
We can also use a table to show these values
What is y when
x = -1 x -1 1 2 3 4 y

5. So there are 4 quadrants, and both x and y can have negative values
The point (0,0) is called the origin

6. At every point on the x axis, y = 0
At every point on the y axis, x = 0
Draw a set of axes from -5 to 5
Draw the line y = 2
Draw the line x = 3
Draw the line y = -1
Draw the line x = -2
Draw the line y = 0
Draw the line x = 0

7. Drawing graphs of linear functions
Linear functions in general come in the form: y=mx = c
This will always produce a straight line.
m is the gradient of the line (how steep it is)
c is the point where the line crosses the y axis. (also known as the y-intercept)

8. Drawing graphs of linear functions
When we know the equation of the line we can create a table for it.
Populate the table with the values of at least 2 points (3 is better)
Plot these points on a graph
Join the points with a straight line

9. Exercise 14.1 Q1, Q2, Q4,
Extension Q11 and Q12
Group activity – on the board complete activity on page 125

10. The gradient (m)
The gradient of a line is found by dividing the distance up by the distance along
Demonstrate the line y = 3x
y=mx = c , in this case the gradient is 3, so m is 3 x -1 1 2 3 4 y -3 6 9 12

11. The intercept (c) In y =mx + c Imagine that x = 0
Remember x = 0 along the y axis.
When x = 0, mx = 0 so you are left with the equation
y = c, so the coordinate shows the point where a straight line crosses the y axis is (0, c)
Exercise 14.2 Q2, Q3, Q4
Extension Q12

12. The gradient intercept method
If you have an equation of a line, you can substitute x= 0 and find where it crosses the y axis
You can also substitute y=0 and to find where it crosses the x axis
Now you have 2 points, you can use this to draw the line (unless they both come to 0, then you’ll need another point aswell)
Exercise 14.3 Q1
Extension Q5

13. Solve linear equations with graphs
Lines with different gradients will cross each other. Here are 2 lines with different gradients
y = x and y = 8 - x
Where the lines cross, the y value and the x value will be the same in both equations
If we substitute the y out, we end up with
x + 1 = 8 – x
We could use algebra to solve for x, or we can draw the lines on a graph and take the coordinates of where they cross on a graph
Ex 14.4 Q1

14. Parallel and perpendicular gradients
Gradients of a parallel line is the sme
Gradients of a perpendicular line is minus the reciprocal
Create an example from gradient of
y = 2x
The gradients of perpendicular lines always multiply together to give -1
Ex 14.5 Q2 Extension Q6

15. Rearranging equations
Sometimes the equations of straight lines are given in other forms.
E.g. px + qy = r
You will be asked to rearrange them into the form y=mx+c
This will come up in the test, so practice a few from Ex14.6

16. Homework Make notes on the ‘what you need to know’ section on page 134
Try a few from review exercise 14
Remember the section reviews which need to be handed in.

17. Section Review Deadlines
Number Section Review - 9th December
Algebra Section Review – 6th January
Shape Space and Measure
Section Review – 14th April
Data Handling Section Review – 5th May