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7.01 Graphing linear functions

Worksheet
Sketch graphs of lines
1

For each of the following linear equations:

i

Find the coordinates of the y-intercept.

ii

Find the gradient.

iii

Sketch the graph using the gradient and y-intercept.

a

y = x + 1

b

y = 4 x-1

c

y = 3 x - 1

d

y = - x + 4

e

y = -6x+2

f

y = - 3 x - 4

g

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

h

y = \dfrac{1}{2} x - 2

2

Sketch the graph of each linear equation using the gradient and y-intercept:

a

2y = 3x-8

b

6x-3y=9

c

2x+5y=0

3

For each of the following, sketch the graph of the line:

a

Which passes through the point \left(0, -10\right) and has a gradient of 5.

b

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

4

Sketch the graph of the following lines given the y-intercept and gradient:

a

A y-intercept of -2 and gradient of 5.

b

A y-intercept of 2 and gradient of - \dfrac{5}{4}.

c

A y-intercept of 7 and gradient of - 1.

d

A y-intercept of - 3 and gradient of - \dfrac{2}{5}.

5

For the following equations:

i

Find the y-intercept.

ii

Find the x-intercept.

iii

Sketch the graph of the line.

a
y = - 4 x + 4
b

3 x + y + 2 = 0

c
- 6 x + 2 y - 12 = 0
6

Consider the equation y = - 2 x.

a

Find the value of the y-intercept.

b

Find the value of the x-intercept.

c

Find the value of y when x = 2.

d

Sketch the graph of the line.

7

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

a

Complete the table of values:

b

Sketch the graph of the line.

c

State the coordinates of the axes intercepts.

d

Find x when y = - 5.

x- 1014
y
8

For each of the following linear equations:

i

Complete the table of values.

ii

Sketch the graph of the line.

a

y = 2 x - 4

x0123
y
b

y = - 2 x + 4

x0123
y
c

y = \dfrac{5 x}{3} - 5

x0369
y
Horizontal and vertical lines
9

Consider the given table for the linear equation x = 0 :

Does this represent the y-axis or x-axis?

x0000
y- 5.5- 2.53.56.5
10

State whether the following statements are true or false for vertical lines:

a

A vertical line's gradient is very large because it is so steep.

b

A vertical line has a gradient that is undefined, because when calculating the gradient using the formula \dfrac{\text{rise }}{\text{run }}, the run is 0 and it is not possible to divide a number by 0.

c

A vertical line's gradient is equal to 0, because when calculating the gradient using the formula \dfrac{\text{rise }}{\text{run }}, the run is 0.

11

State whether the following statements are true or false when the gradient of a line is zero:

a

The line is horizontal.

b

The line is vertical.

c

The change in y is equal to zero.

d

The change in x is equal to zero.

e

The change in y is equal to the change in x.

12

Consider the graphed line below:

a

State the gradient of the line.

b

Does this line have a y-intercept?

c

State the x-intercept of the line.

d

Hence write the equation of the line.

-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
13

Consider the graphed line below:

a

Complete the table of values for the line:

x-3 014
y
b

Hence state the equation of the line.

-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
14

For the following graphs:

i

State the coordinates of the y-intercept.

ii

State the gradient of the line.

iii

Write the equation of the line.

a
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
b
-5
-4
-3
-2
-1
1
2
3
4
5
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
c
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
d
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
15

Consider the graphed line below:

a

Complete the table of values for the line:

x
y310-2
b

Hence state the equation of the line.

-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
16

Sketch the graph of the following linear equations:

a

y = 4

b

x = 1

c

x = 0

d

y = 0

e

y = \dfrac{3}{2}

f

x = 4.5

g

y = - 3

h

x = - 6

i

x = - 8

17

State the equation of:

a

The x-axis.

b

The y-axis.

18

State the coordinates of the point of intersection of the following:

a

The line y = 5 and the line x = -2.

b

The horizontal line with y-intercept of 9 and the vertical line with x-intercept of -7.

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