1 / 12

Graphs for GCSE Maths

Graphs for GCSE Maths. x and y co-ordinates. E very 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). L et’s draw a grid and add scale numbers ….

luigi
Download Presentation

Graphs for GCSE Maths

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Graphsfor GCSE Maths David Weeks, Mathsmadeeasy

  2. 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) Let’s draw a grid and add scale numbers … So (1,2) is one along the x scale from zero and two along the y scale from zero Where is (2, 3)? Or ( -2, 4) Or (-1,-4) So, that’s co-ordinates. Lets look at connecting them together … Or (4,-3) David Weeks, Mathsmadeeasy

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

  4. y=1/2x So, y=x is at 450 clockwise from the y scale y=-1/2x y=x y=-x y=2x Line equations connecting x and y Lets say we have an equation y=x. Give some co-ordinates on this line. (0,0),(1,1), (2,2),(-1,-1), (-2,-2) Draw this line equation 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 David Weeks, Mathsmadeeasy

  5. Equation Gradient y=1/2x y=-1/2x y=x y=2x y=-2x y=-x Working out the Gradient y=mx What are the gradients of the lines below y=x y=-x y=2x y=-2x y=½ x y=-½x 1 -1 2 -2 ½ -½ Positive Negative Gradient 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 David Weeks, Mathsmadeeasy

  6. y y y 2 3 3 x x x 3 3 1 3 3 2 change in y change in y change in y Gradient = Gradient = Gradient = 1 3 3 change in x change in x change in x Gradient = Gradient = Gradient = Gradient = 1 Gradient = 2/3 Gradient = 3 Gradient means steepness Gradient = change in vertical divided by change in horizontal David Weeks, Mathsmadeeasy

  7. y y y 2 3 3 x x x 3 3 1 2 3 3 change in y change in y change in y Gradient = Gradient = Gradient = 3 3 1 change in x change in x change in x Gradient = Gradient = Gradient = Gradient = -2/3 Gradient = -3 Gradient = -1 Gradient = change in vertical divided by change in horizontal Gradient can be negative David Weeks, Mathsmadeeasy

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

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

  10. Gradient Y/X Equation Crosses Y 1 1/2 1 -2 -1 -2 2 Y=x - 1 Y=-2x - 2 Y=½x + 2 2 3 1 3 2 Working out the equation of a line y=mx+c Work out the equations of these lines 1. Record where it crosses the y scale. This is called c 2. Work out the gradient, called m 3. Put the two together as: Y = mx + 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 David Weeks, Mathsmadeeasy

  11. 4 1 2 3 5 Match the equations y=x-4 y=2x+3 y=-x+1 y=-2x-1 y=3x-2 David Weeks, Mathsmadeeasy

  12. 4 2 3 5 Your Turn - What’s the equations 1 Notice the gradients when lines are at right angles or perpendicular (2 & 3) David Weeks, Mathsmadeeasy

More Related