PowerPoint Presentation

StarterOn your MINI WHITE-BOARDS

LO: Investigate how to find the gradient of a line given two coordinatesTo be able to plot coordinates in all four quadrantsTo be able to find the gradient of a line from a graphTo be able to find the gradient given only two coordinatesGRADIENTS

Make the following triangles by plotting the coordinates and joining them together:

Triangle A (1,1), (4,1), (4,4)

Triangle B (-1,1), (-3,1), (-1,3)

Triangle C(-1,-2), (-1,-4), (-5,-4)

Triangle D(3,0), (2,-5), (3,-5)

Extension Triangle E (-5,-2), (-3,-2), (-5,2)

Make the following triangles by plotting the coordinates and joining them together:

Triangle A (1,1), (4,1), (4,4)

Triangle B(-1,1), (-3,1), (-1,3)

Triangle C(-1,-2), (-1,-4), (-5,-4)

Triangle D(3,0), (2,-5), (3,-5)

Extension Triangle E (-5,-2), (-3,-2), (-5,2)

ADCBE

What is the same and what is different about these triangles?

Triangle A (1,1), (4,1), (4,4)

Triangle B(-1,1), (-3,1), (-1,3)

Triangle C(-1,-2), (-1,-4), (-5,-4)

Triangle D(3,0), (2,-5), (3,-5)

Extension Triangle E (-5,-2), (-3,-2), (-5,2)

ADCBE

What is the same and what is different about these triangles?

Triangle A

Triangle B

Triangle C

Triangle D

Extension Triangle E

ADCBE

The gradient of a line is a number representing its slope.

xThis line has a gradient of 0This line has a gradient of 1The gradient of this almost vertical line has a gradient of 10How are these numbers calculated?This vertical line has an infinite gradient.

xWe draw a triangle under the line, and calculate the value of

upacrossSo this line has a gradient of 2

What is the gradient of each of these triangles?

Triangle A

Triangle B

Triangle C

Triangle D

Extension Triangle E

ADCBE

x

Work out the gradient of the line joining (2,1) and (4,5)Plot the points(2,1)(4,5) Draw a triangle and work out the length of each side.

You must remember to do the subtractions in the same order!24

xWork out the gradient of the line joining (4,0) and (-2,5)Plot the points(-2,5)(4,0) Draw a triangle and work out the length of each side.

You must remember to do the subtractions in the same order!-65

ON YOUR MINI-WHITEBOARDSWork out the gradient of the line joining (3,2) and (4,5)- Plot the points- Draw a triangle and work out the length of each side.Remember to do the subtractions in the same order!

xWork out the gradient of the line joining (3,2) and (4,5)Plot the pointsDraw a triangle and work out the length of each side.

(3,2) (4,5)4 3 = 1 15 2 = 3 3

ON YOUR MINI-WHITEBOARDSWork out the gradient of the line joining (2,-5) and (4,3)- Plot the points- Draw a triangle and work out the length of each side.Remember to do the subtractions in the same order!

Work out the gradient of the line joining (2,-5) and (4,3)Plot the pointsDraw a triangle and work out the length of each side.4 2 = 2 (2,-5) (4,3)

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End

EasyMediumHard

What have we learntTo be able to plot coordinates in all four quadrantsTo be able to find the gradient of a line from a graphTo be able to find the gradient given only two coordinates

xYour turnPlot the coordinates (1,5) and (-1,-5)

Join them together to make a straight line

Draw a right-angled triangle under this line and calculate its gradient

102

xYour turn

102

upacrossSo this line has a gradient of 5

xWhat are the gradients of these lines?Blue line Red line Green line Orange line Black line

What is the same and what is different about these lines?

252-1-

1) Find the gradient between the points:(3,5) and (4,7)(5,9) and (7,17)(4,6) and (5,7)(1,4) and (4,19)(0,11) and (4,23)2) Find the gradient between these points:(2,5) and (3,-3)(2,8) and (3,2)(4,8) and (8,4)(8,15) and (6,33)(7,12) and (4,42)(4,8) and (3,14)Find the gradient between these points:(3,5) and (4,5.5)(5,9) and (7,8)(4,6) and (5,6.75)(1,4) and (4,4.75)(0,11) and (4,11.4)Answers 2 4 1 5 3 -8 -6 -1 -9 -10 -6 0.5 -0.5 0.75 0.25 0.1

xWhat are the gradients of these lines?Blue line Red line Green line Orange line Black line

What is the same and what is different about these lines?

xWhat are the gradients of these lines?Blue line Red line Green line Orange line Black line

What is the same and what is different about these lines?

1) Find the gradient between the points:(3,5) and (4,7)(5,9) and (7,17)(4,6) and (5,7)(1,4) and (4,19)(0,11) and (4,23)2) Find the gradient between these points:(2,5) and (3,-3)(2,8) and (3,2)(4,8) and (8,4)(8,15) and (6,33)(7,12) and (4,42)(4,8) and (3,14)Find the gradient between these points:(3,5) and (4,5.5)(5,9) and (7,8)(4,6) and (5,6.75)(1,4) and (4,4.75)(0,11) and (4,11.4)1) Find the gradient between the points:(3,5) and (4,7)(5,9) and (7,17)(4,6) and (5,7)(1,4) and (4,19)(0,11) and (4,23)2) Find the gradient between these points:(2,5) and (3,-3)(2,8) and (3,2)(4,8) and (8,4)(8,15) and (6,33)(7,12) and (4,42)(4,8) and (3,14)Find the gradient between these points:(3,5) and (4,5.5)(5,9) and (7,8)(4,6) and (5,6.75)(1,4) and (4,4.75)(0,11) and (4,11.4)

x