�2 9.1 Drawing straight-line graphs by plotting points

1

1 On Resource sheet 9.1a draw and label lines with equations:

a x = 4 b x = −2 c y = 1 d y = 0.

2 Write down the equation of the four lines that form the sides of the rectangle ABCD.

The equation of line AB is .......................................................................................................................................................................

The equation of line BC is .......................................................................................................................................................................

The equation of line CD is .......................................................................................................................................................................

The equation of line DA is .......................................................................................................................................................................

3 Using Resource sheet 9.1b

a complete the table of values for y = x + 2

b draw the graph of y = x + 2.

Guided practice worksheet

127A

3 4 5 x2

3

5

4

y

2

1

–1

–2

–3

–4

–5

1–1–2–3–5 –4 0

D A

BC

Questions are targeted at the grades indicated

�2 9.1 Drawing straight-line graphs by plotting points

2

Guided practice worksheet

127B

4 Using Resource sheet 9.1c

a complete the table of values for y = x − 3.

b draw the graph of y = x – 3.

c write down the value of y when x = 3.

5 Using Resource sheet 9.1d

a complete the table of values for y = 3x + 1

b draw the graph of y = 3x + 1.

6 Using Resource sheet 9.1e, draw the graph of y = 4 − 3x for values of x from −2 to +3.

7 Using Resource sheet 9.1f, draw the graphs of:

a x + y = −3 b 3x +2y = 6

8 Match each of the equations with its graph.

a y = −x b x + y = 4 c y = 4x d y = x + 4 e y = x − 4

3 4 5 x2

3

5

4

EA

C

B

D

y

2

1

–1

–2

–3

–4

–5

1–1–2–3–5 –4 0

C

�2 9.2 Finding the midpoint of a line segment

129A

The midpoint of a line is halfway along the line.

To find the coordinates of the midpoint of a line joining two points, you work out the mean of the x-coordinates and the mean of the y-coordinates.

1 On the diagrams below, mark with a cross, the midpoint of each line segment. Label it M.

a b

M ( ......................................... , ......................................... ) M ( ......................................... , ......................................... )

c d

M ( ......................................... , ......................................... ) M ( ......................................... , ......................................... )

In each case write down the coordinates of M.

Guided practice worksheet

0 1

1

–1

2

3

2 3 4 5

y

x

0 1–1–2–3

1

–1

–2

–3

2

3

2 3

y

x

0 1–1–2–3

1

–1

–2

–3

2

3

2 3

y

x

0 1–1–2–3

1

–1

–2

–3

2

3

2 3

y

x

D

Questions are targeted at the grades indicated

�2 9.2 Finding the midpoint of a line segment

129B

Guided practice worksheet

2 Complete the following statements:

a Point A is (2, 3). Point B is (6, 9).

The coordinates of the midpoint of AB are 2 62

3 92

+ +( ), = (4, ...........................)

b Point D is (−4, 2). Point E is (0, 8).

The coordinates of the midpoint of DE are –4 02+( ), ––––––––––4 0

2+( ) = (........................... , ...........................)

c Point P is (1, 6). Point Q is (5, 8).

The coordinates of the midpoint of PQ are (........................... , ...........................) = (........................... , ...........................)

d Point S is (2, −4). Point T is (9, 8).

The coordinates of the midpoint of ST are (........................... , ...........................) = (........................... , ...........................)

3 N is the midpoint of the line joining V (−3, 5) to W (5 −9).

Work out the coordinates of N.

N (......................................... , .........................................)

C

�2 9.3 The gradient and y-intercept of a straight line

131A

1 Complete the following calculations to work out the gradient of each line. Each square represents one unit.

Gradient = 42

Gradient = — Gradient = —

= ................... = ................... = ...................

Gradient = –62

Gradient = — Gradient = —

= ................... = ................... = ...................

Gradient of a line = change in y direction––––––––––––––––––––change in x direction

The y-intercept is where the graph crosses the y-axis.

Change in xdirection

Change in ydirection

y

x0

positive gradient negative gradient

Guided practice worksheet Questions are targeted at the grades indicated

�2 9.3 The gradient and y-intercept of a straight line

131B

2 Work out the gradient of each line.a b

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

3 Work out the gradient of each line. Remember to take the scales on the axes into account.a b

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

c Write down the coordinates of the y-intercept for the graph in a.

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

d Write down the coordinates of the y-intercept for the graph in b.

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

4 Find the gradient and coordinates of the y-intercept for each line.a b

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

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

x

y

1

2

3

4

5

6

7

8

10 2 3 4 5 6 7 8x

y

1

2

3

4

5

6

7

8

10 2 3 4

x

y

5

10

15

10 2 3 4 5x

y

1

2

3

20 4 6 8

x

y

1

2

3

4

5

6

7

–1

–2

–3

–4

1 2 3 4 5–1–2 0x

y

2

–2

–4

–6

–8

–2–4–6 0 2 4 6

x

y

1

2

3

4

5

6

7

–1

–2

–3

–4

1 2 3 4 5–1–2 0x

y

2

–2

–4

–6

–8

–2–4–6 0 2 4 6

Guided practice worksheet

D

�2 9.4 The equation y = mx + c

1 Write down the gradient and y-intercept of the lines with equations

a y = 4x + 7

Gradient = ......................................................................

y-intercept = ......................................................................

b y = −2x

Gradient = ......................................................................

y-intercept = ......................................................................

c y = 1 −1–3 x

Gradient = ......................................................................

y-intercept = ......................................................................

2 Write down the equation of the line that has gradient 3 and y-intercept −10.

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

3 Find the gradient of the lines

a 2y = x

Gradient = ..................................................................

b 2x + y = 8

Gradient = ..................................................................

4 Find the coordinates of the y-intercept of the lines in question 3.

a y-intercept = (....................., .....................)

b y-intercept = (....................., .....................)

5 Write down the equation of the line which has gradient − 12 and passes through the point (0, 4).

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

133

The line y = mx + c, where m and c are numbers, has gradient m and y-intercept c.

Guided practice worksheet

C

A

Questions are targeted at the grades indicated

�2 9.5 Parallel and perpendicular lines

135A

If a line has a gradient m, then any parallel line also has gradient m.

Two lines are perpendicular to each other if they intersect at right angles.

If a line has a gradient m, then any line perpendicular to it has gradient – 1m.

1 Here is a line l1. The gradient of the line is 1.

On the grid, draw two more lines which have gradient 1.

2 The gradient of the line l2 is − 12 .

On the grid, draw two more lines

which have gradient − 12

3 In the table, in each case, write down the equation of any line parallel to the line whose equation is given.

The first one is done for you.

a y = 2x + 3 y = 2x + 5

b y = −5x + 2

c y = − 13x + 5

d y = x − 6

e y = 3 − 2x

Guided practice worksheet

0 1–1–2–3

1

–1

–2

–3

2

3

2 3

yl1

x

0 2–2–4–6

2

–2

–4

–6

4

6

4 6

y

l2

x

D

C

Questions are targeted at the grades indicated

�2 9.5 Parallel and perpendicular lines

135B

Guided practice worksheet

4 The gradient of the line l3 is 3.

On the grid draw a line perpendicular to l3.

Complete the statement: The gradient of the line I have drawn is

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

5 The gradient of the line l4 is − 12 .

On the grid draw a line perpendicular to l4.

Complete the statement: The

gradient of the line I have drawn is

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

6 In the table, in each case, write down the equation of any line perpendicular to the line whose equation is given.

a y = 3x – 1

b y = −2x + 7

c y = 14x – 5

d y = 110x + 1

e y = 4 − x

0 1–1–2–3

1

–1

–2

–3

2

3

2 3

yl3

x

0 2–2–4–6

2

–2

–4

–6

4

6

4 6

y

l4

x

B

�2 9.6 Real-life graphs

137A

1 Amanda went for a walk to her friend’s home. She caught the bus back home.

The distance–time graph shows this.

Use the graph to answer the following questions.

a Which section of the graph represents

i Amanda walking to her friend’s house? ..................................................................

ii the time Amanda spent at her friend’s house? ..................................................................

iii the bus journey back home? ..................................................................

b Amanda spent ............................. minutes at her friend’s house.

c i The distance Amanda had to walk to her friend’s house was ............................. km.

ii The time taken for Amanda to walk to her friend’s house was ............................. hours.

iii Amanda’s walking speed between her house and her friend’s house was ............................. km/h.

d The speed of the bus on the journey home was ............................. km/h.

Guided practice worksheet

0

1

2 pm1 pm 3 pm 4 pm 5 pm 6 pm

Time of day

2

3

4

5

6

Dist

ance

from

hom

e (k

m)

y

xA

B C

D

C

Questions are targeted at the grades indicated

�2 9.6 Real-life graphs

137B

2 Liquid is poured at a constant rate into each of the containers shown below.

The sketch graphs show how the height of the liquid changes with time.

By drawing a line, match each container with one of the graphs below.

a i

b ii

c iii

Guided practice worksheet

(i)(a)

(ii)(b) (ii)(b)

(ii)(c) (ii)(c)

(i)(a)

C

139

�2 9.7–9.8 Compound measures and speed

1 Which of the following are units of compound measures?

km/hr metres g/cm3 kg l/km

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

2 A car travels 220 miles and uses 40 litres of petrol. Work out the average fuel consumption of the car.

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

3 A production line in a factory produces 480 units in an eight-hour shift.

a Calculate the average rate of production, giving your answer in units/hr.

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

b The factory receives an order for 10 000 units. Calculate to the nearest whole number the number of shifts required to complete the order.

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

4 Karen drives to Manchester, a distance of 210 km, in three and a half hours.

a Calculate her average speed for the journey.

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

b She then travels to Leeds at the same average speed. The journey takes one hour and 20 minutes. Calculate the distance between Manchester and Leeds.

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

5 Luki estimates that on a long journey he can cycle at an average speed of 30 km/hr.

a How long should Luki allow to complete a journey of 260 km?

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

b Luki completes the journey in six and a half hours. What was his actual average speed for the trip?

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

Guided practice worksheet

D

Questions are targeted at the grades indicated