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Middle Years

4.04 Linear graphs

Worksheet
Tables of values method
1

Consider the equation y = 2 x - 4.

a

Complete the table of values:

x0123
y
b

Sketch the line that passes through these points.

2

For each of the following equations:

i

Complete a table of values of the form:

x- 1012
y
ii

Sketch the graph of the line on a number plane.

a

y = x + 9

b

y = 3 x + 3

c

y = 4 x

d

y = - x + 1

e
y = 3 x - 4
f
y = 2 x +5
g
y = 4- x
h
y = -2x+ 8
3

For each of the following equations:

i

Complete the table of values:

x- 3036
y
ii

Sketch the graph of the line on a number plane.

a

y = - 3 x -1

b

y = \dfrac{x}{3} + 2

4

Consider the equation y = - \dfrac{3 x}{2} + 6.

a

Complete the table of values:

x- 2024
y
b

Sketch the graph of the line on a number plane.

5

Consider the equation y = - x - 2.

a

Complete the table of values:

x- 101
y
b

Sketch the line on a number plane.

c

Find the coordinates of the y-intercept.

d

Find the coordinates of the x-intercept.

e

Find the y-value when x = 3.

f

Find the x-value when y = -4.

6

Consider the equation 2 x - 3 y - 18 = 0.

a

Complete the table of values:

x- 303
y
b

Sketch the line on a number plane.

c

Find the coordinates of the y-intercept.

d

Find the coordinates of the x-intercept.

e

Find the y-value when x = 6.

Gradient and one point method
7

Sketch the following lines on a number plane:

a

A line that passes through the point \left( - 1 , 2\right) and has a gradient of 4.

b

A line that passes through the point \left( - 1 , 8\right) and has a gradient of - 2.

c

A line that passes through the point \left(3, 5\right)and has a gradient of 5.

d

A line that passes through the point \left( - 2 , 4\right) and has a gradient of- 3.

8

For each of the following equations of lines:

i

Find the gradient of the line.

ii

Find the coordinates of the point on the line where x=0.

iii

Sketch the line on a number plane.

a

y = 3 x - 3

b

y = - 2 x -1

c

y = x - 1

d
y = \dfrac{x}{3} + 3
e
6 x - 3 y + 18 = 0
f
- 6 x + 3 y + 24 = 0
Intercepts method
9

For each of the following equations of lines:

i

Find the x-intercept of the line.

ii

Find the y-intercept of the line.

iii

Sketch the line on a number plane.

a
y = x + 1
b
y = 3 x - 1
c
y = - x + 4
d
y = - 5x - 4
10

For the following linear equations:

i

Find the coordinates of the y-intercept.

ii

Find the coordinates of the x-intercept.

iii

Sketch the line.

a

y = 2 x - 2

b

y = - 2 x + 4

c

y = - \dfrac{4 x}{3}

d

y = - 3 x + 6

11

For each of the following equations:

i

Find the y-value of the y-intercept of the line.

ii

Find the x-value of the x-intercept of the line.

iii

Find the value of y when x = -1.

iv

Sketch the equation of the line on a number plane.

a
y = - 2 x
b
y = x - 2
12

Sketch the following lines using the y-intercept and any other point on the line:

a

y = x + 5

b

y = 3 x - 4

c

y = - x - 5

d

y = - 4x + 7

13

Find the x-intercept of the line - x - 8 y = 8.

14

For each of the following equations:

i

Solve for the x-intercept of the line.

ii

Solve for the y-intercept of the line.

iii

Sketch the line on a number plane.

a

3 x + y - 1 = 0

b

- 6 x + 2 y + 18 = 0

c
8 x + 2 y - 16 = 0
d
- 20 x + 5 y - 40 = 0
Gradient-intercept method
15

Sketch the following lines using the gradient and y-intercept:

a
y = 4 x-1
b
y = \dfrac{1}{2} x - 2
16

Sketch the following lines on a number plane:

a

A line that has a y-intercept of - 2 and whose gradient is 4.

b

A line that has a y-intercept of 8 and whose gradient is - 4.

c

A line that has a y-intercept of 2 and whose gradient is \dfrac{1}{2}.

d

A line that has a y-intercept of 7 and whose gradient is - \dfrac{3}{4}.

e

A line that has an x-intercept of 3 and whose gradient is 2.

f

A line that has an x-intercept of - 2 and whose gradient is 3.

g

A line that has an x-intercept of - 5 and whose gradient is - 3.

h

A line that has an x-intercept of - 8 and whose gradient is - 1.

Horizontal and vertical lines
17

Sketch the following lines on the number plane:

a

y = 3

b

x = 7

c

y = - 5

d

x = - 6

e

y = 8

f

x = 7

g

y = - 2

h

y = 0

18

Sketch the following lines:

a

The line parallel to the x-axis and passes through the point \left(3, - 5 \right).

b

The line parallel to the y-axis and passes through the point \left( - 8 , 3\right).

c

The line perpendicular to the x-axis and passes through the point \left(3, - 8 \right).

d

The line perpendicular to the y-axis and passes through the point \left(3, - 4 \right).

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