Session 10 – Straight Line Graphs GCSE Maths

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

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

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

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

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)

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

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

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

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

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

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

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

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

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.

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