GCSE Maths

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

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

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 + 1 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