9.2 gradients - pearson levelle homework questions · c line 3: gradient = = −3 d line 4:...

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9.2 Gradients 1 a Complete this table for the equation y = 2x − 3.

x −2 −1 0 1 2

y −7

b Plot your points from your table and draw a straight line through your points.

2

a Which of the line segments in the diagram have:

i a positive gradient ......................

ii a negative gradient? ......................


b Work out the gradient of each of the line segments in the diagram.

line 1 .....................................................................................................................................

line 2 .....................................................................................................................................

line 3 .....................................................................................................................................

line 4 .....................................................................................................................................

line 5 .....................................................................................................................................

line 6 .....................................................................................................................................

3

a Complete the table of values for each graph. Use the completed tables to plot each graph. Label each graph with its equation.

i y = x + 3

x −2 −1 0 1 2 3

y 1 2

ii y = 3x − 2

x −2 −1 0 1 2 3

y −5 −2

iii y = −2x + 5

x −2 −1 0 1 2 3

y 9

b Calculate the gradient of each graph.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

c From your tables, look at the sequence for the y values. How does this connect to the gradient?

..............................................................................................................................................

d From the equations, look at the coefficient of x. How does this connect to the gradient?

..............................................................................................................................................


9.2 Gradients 1 a i Plot a graph by using the values

from the table.

x −2 −1 0 1 2

y −7 −4 −1 2 5

ii Work out the gradient of your graph from part i.

..................................................

b i Swap the x- and y-values and plot a new graph on the same axes.

ii Work out the gradient of the new line.

..................................................

c i Plot a graph by using the values from the table.

x −2 −1 0 1 2

y −5 −3 −1 1 3

ii Work out the gradient of your graph from part i.

..................................................

d i Swap the x- and y-values and plot a new graph on the same axes.

ii Work out the gradient of the new line.

..................................................

e Look at your gradients. Is there a connection between the original gradients and the gradients of the new lines? ......................


2 a Use the graph to complete the table below.

x −2 −1 0 1 2

y-values (A)

y-values (B)

b What is the gradient of each line?

line A ......................

line B ......................

c What is the mathematical relationship between lines A and B?

..............................................................................................................................................


9.2 Gradients 1

Complete each statement. Use the diagram to help.

The first one has been done for you.

a Line 1 goes 3 units up for every 1 unit to the right.

b Line 2 goes ……. unit(s) up for every ……. unit(s) to the right.

c Line 3 goes ……. unit(s) up for every ……. unit(s) to the right.

d Line 4 goes 2 units down for every ……. unit(s) to the right.

e Line 5 goes ……. unit(s) down for every ……. unit(s) to the right.

f Line 6 goes ……. unit(s) down for every ……. unit(s) to the right.

2 Using your answers to Q1, complete to work out the gradient of each line.

a Line 1: gradient = = 3 b Line 2: gradient = = …….

c Line 3: gradient = = ……. d Line 4: gradient = = …….

e Line 5: gradient = = ……. f Line 6: gradient = = …….

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3

Complete each statement. Use the diagram to help.

a Line 1 goes ……. unit(s) up for every ……. unit(s) to the right.

b Line 2 goes ……. unit(s) up for every ……. unit(s) to the right.

c Line 3 goes ……. unit(s) down for every ……. unit(s) to the right.

d Line 4 goes ……. unit(s) down for every ……. unit(s) to the right.

4 Using your answers to Q3, complete to work out the gradient of each line.

a Line 1: gradient = = …….

b Line 2: gradient = = …….

c Line 3: gradient = = …….

d Line 4: gradient = = …….

5 For Q3 a student says, ‘Line 4 has a negative gradient.’ Is the student correct? Explain how you know.

....................................................................................................................................................


9.2 Gradients Core 1 a b

x −2 −1 0 1 2

y −7 −5 −3 −1 1

2 a i Lines 1, 3 and 4 ii Lines 2, 5 and 6

b Line 1 = 2, line 2 = −3, line 3 = 1,

line 4 = , line 5 = −1 and line 6 =

3 a i x −2 −1 0 1 2

y 1 2 3 4 5

ii

x −2 −1 0 1 2

y −8 −5 −2 1 4

iii

x −2 −1 0 1 2

y 9 7 5 3 1

b Gradients are 1, 3 and −2

c For i), the y-values increase by 1 and the gradient is 1. For ii), the y-values increase by 3 and the gradient is 3. For iii), the y-values decrease by 2 and the gradient is −2.

d The gradient matches the coefficient of x.

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Depth 1 a i See graph

ii Gradient = 3

b i See graph

ii Gradient =

c i See graph

ii Gradient = 2

d i See graph

ii Gradient =

e The new gradients are the reciprocals of the original gradients.

2 a

x −2 −1 0 1 2

y-values (A) 3 1 −1 −3 −6

y-values (B) −2 −1.5 −1 0.5 0

b The gradient of line A is −2.

The gradient of line B is

c The lines are perpendicular to each other.

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Support 1 b Line 2 goes 1 unit up for every 2 units to the right.

c Line 3 goes 4 units up for every 1 unit to the right.

d Line 4 goes 2 units down for every 1 unit to the right.

e Line 5 goes 1 unit down for every 3 units to the right.

f Line 6 goes 4 units down for every 1 unit to the right.

2 a Line 1: gradient = = 3 b Line 2: gradient = =

c Line 3: gradient = = 4 d Line 4: gradient = = −2

e Line 5: gradient = = f Line 6: gradient = = −4

3 a Line 1 goes 2 units up for every 1 unit to the right.

b Line 2 goes 1 unit up for every 3 units to the right.

c Line 3 goes 3 units down for every 1 unit to the right.

d Line 4 goes 1 unit down for every 2 units to the right.

4 a Line 1: gradient = = 2 b Line 2: gradient = =

c Line 3: gradient = = −3 d Line 4: gradient = =

5 Yes, the student is correct. The line slopes downwards so has a negative gradient. Alternatively, from Q4 we can see the value is a negative number.

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9.2 gradients - pearson levelle homework questions · c line 3: gradient = = −3 d line 4:...

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