Graphs

Graphsfor GCSE Maths : 

David Weeks, Mathsmadeeasy Graphsfor GCSE Maths

x and y co-ordinates : 

David Weeks, Mathsmadeeasy x and y co-ordinates Every point on the grid can be found with two numbers. One along the vertical scale labelled y and one on the horizontal scale labelled x These are called co-ordinates (x, y) Where is (2, 3)? Or ( -2, 4) Or (-1,-4) Or (4,-3) So (1,2) is one along the x scale from zero and two along the y scale from zero Let’s draw a grid and add scale numbers … So, that’s co-ordinates. Lets look at connecting them together …

Connecting co-ordinates – line equations : 

David Weeks, Mathsmadeeasy Connecting co-ordinates – line equations Lets think about the co-ordinates where y = 2. What could they be? Draw the line y=1 Or y=-4 Now try x=3 and x=-2 If we connect these points we get a horizontal line and everywhere along the line y=2. So, the line equation is Y=2 We have drawn simple equations , Lets look at equations that link x and y together … (1,2), (3,2), (5,2) (-1,2),(-4, 2)

Line equations connecting x and y : 

David Weeks, Mathsmadeeasy Line equations connecting x and y Lets say we have an equation y=x. Give some co-ordinates on this line. Draw the line y=2x Or y=-x Now try y=1/2 x Or y= -1/2x Notice that as the number in front of x gets bigger the line gets steeper. This is the GRADIENT. For y=x, gradient =1, y=2x, gradient = 2 (0,0),(1,1), (2,2),(-1,-1), (-2,-2) Draw this line equation

Working out the Gradient y=mx : 

David Weeks, Mathsmadeeasy Working out the Gradient y=mx What are the gradients of the lines below Notice that y=-x has a negative gradient of 450 anticlockwise from the y scale Negative gradients point to the left, positive gradients point to the right y=x y=-x y=2x y=-2x y=½ x y=-½x 1 -1 2 -2 ½ -½ Positive Negative Gradient

Gradient means steepness : 

David Weeks, Mathsmadeeasy Gradient means steepness Gradient = change in vertical divided by change in horizontal

Gradient can be negative : 

David Weeks, Mathsmadeeasy Gradient can be negative

Find the gradient from two points : 

David Weeks, Mathsmadeeasy Find the gradient from two points (2,2) and (-2,0) (-3-4) and (3,0) (-5,4) and (-3,-2) Work out the gradients of these pairs of co-ordinates 1. Draw a triangle as shown 2. Note the length of the x side and the y side of the triangle and divide one by the other to get the gradient Y side = 4 X side = 6 Grad = 4/6 Y side = 2 X side = 4 Grad = ½ Y side = 6 X side = 2 Grad = 3 Which gradient is negative?

Your turn - Find the gradient from two points : 

David Weeks, Mathsmadeeasy Your turn - Find the gradient from two points (3,3) and (-1,-3) (-4-1) and (3,0) (-1,4) and (2,-2) Work out the gradients of these pairs of co-ordinates

Working out the equation of a line y=mx+c : 

David Weeks, Mathsmadeeasy Working out the equation of a line y=mx+c 1. Record where it crosses the y scale. This is called c So you can find the equation of a line by using its gradient and where it crosses the Y scale and putting them in the equation y=mx+c Work out the equations of these lines 2. Work out the gradient, called m 3. Put the two together as: Y = mx + c

Match the equations : 

David Weeks, Mathsmadeeasy Match the equations y=2x+3 y=-x+1 y=-2x-1 y=3x-2 y=x-4

Your Turn - What’s the equations : 

David Weeks, Mathsmadeeasy Your Turn - What’s the equations 1 Notice the gradients when lines are at right angles or perpendicular (2 & 3)