9.3 equations of straight lines · 9.3 equations of straight lines core 1 a ba d and and e ab b,d...

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9.3 Equations of straight lines 1 Look at these equations of graphs.

A y = 3x + 2 B y = −x + 2 C y = x − 7

D y = 3x − 4 E y = −x − 4 F y = 3x + 1

Which of the graphs:

a have the same y-intercept ......................

b are parallel? ......................

2

a Match each graph to an equation.

y = 2x ......................

y = 3 ......................

y = x + 3 ......................

y = 3x – 4 .................... ..

y = x − 2 ......................

b Which graphs are parallel? ......................

c Which graphs pass through the origin? ......................

d Write the equation of a line parallel to graph D. ......................


3 Write the equations of these graphs.

A ................................................................................................................................................

B ................................................................................................................................................

C ................................................................................................................................................

D ................................................................................................................................................

E ................................................................................................................................................

F ................................................................................................................................................


9.3 Equations of straight lines 1 Which of these graphs show direct proportion? ......................

A y = 2x − 4 B y = −3x C y = x D y = −x + 3 E y = x

2 For each of the equations given, write the gradient and the y-intercept. Equation of the line Gradient y-intercept

y = 2x + 3

y = x − 5

y = −2x − 4

y = 5 − x

y = 3x + 8

y = x + 3

3 A rectangle is made using four straight lines. The equation of line A is y = −2x + 7. Write the equations of the other three lines.

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

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

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4 Decide if each of these statements about y = 2x − 3 is true or false.

a It crosses the y-axis at (2, −3) ......................

b It has a gradient of 2 ......................

c It is parallel to y − 2x = 7 ......................

d It is a reflection in the y-axis of y = −2x − 3 ......................

5 A line meets the y-axis at (0, 4). Write down three different possible equations for the line.

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


9.3 Equations of straight lines 1 Use the diagram to find:

a i the gradient of line 1 ............................

ii the y-intercept of line 1 ............................

b i the gradient of line 2 ............................

ii the y-intercept of line 2. ............................

c Use these answers to write down the equations of lines 1 and 2.

Line 1: y = …….x − …….

Line 2: y = …….x + …….

2 Complete the table for the four lines.

Line Gradient y-intercept equation

1 y = …….x + …….

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9.3 Equations of straight lines Core 1 a A and B D and E b A, D and F B and E

2 a y = 2x is D, y = 3 is A, y = x + 3 is B, y = 3x − 4 is E and y = x – 2 is C. b Graphs B and C c D d Any equation with y = 2x; for example, y = 2x + 4 or y = 2x − 1

3 A is y = x + 3, B is y = 2x + 6, C is y = −x − 2, D is y = 3x + 1, E is y = x − 4 and F is y = −x + 5

Depth 1 B, C and E

2 Equation of the line Gradient y-intercept

y = 2x + 3 2 3

y = x − 5 1 −5

y = −2x − 4 −2 −4

y = 5 − x −1 5

y = 3x + 8 3 8

y = x + 3 3

3 B is y = x + 5, C is y = x − 2 and D is y = −2x − 5

4 a False b True c True d True

5 Students’ own answers, such as y = 4, y = x + 4, y = −x + 4, y = 2x + 4.

Support 1 a i Gradient = 1 ii y-intercept = −2

b i Gradient = −2 ii y-intercept = 1 c Line 1: y = x − 2, Line 2: y = −2x + 1

2 Line Gradient y-intercept Equation

1 −1 4 y = −x + 4

2 −2 1 y = −3x + 1

3 1 5 y = x + 5

4 2 −1 y = 2x − 1

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9.3 equations of straight lines · 9.3 equations of straight lines core 1 a ba d and and e ab b,d...

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