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Middle Years

10.03 Graphs of linear equations

Worksheet
Intercepts
1

For each of the following graphs:

i

State the value of the x-intercept.

ii

State the value of the y-intercept.

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

Given each linear equation and its graph, state the coordinates of the y-intercept:

a
y = 4x - 5
-4
-3
-2
-1
1
2
3
4
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
y
b
y = \dfrac{x}{2} + 3
-6
-4
-2
2
4
6
x
-2
2
4
6
8
y
3

Consider the following graph of the line y = - 2 x + 3:

a

State the the y-value, when x is 0.

b

Explain the relationship between the value of the y-intercept and the equation of the line.

c

If the equation of a line is y = m x + c, state the value of the y-intercept.

-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
5
6
7
y
4

Consider the following three linear equations and their corresponding graphs:

y = x + 4, \, y = 2 x + 4, \, y = 4 x + 4

a

What do all of the equations have in common?

b

What do all of the graphs have in common?

c

What conclusion can be made about lines that have the form y = m x + 4?

-8
-6
-4
-2
2
4
6
8
x
-4
-2
2
4
6
8
10
y
5

Find the value of the y-intercept of the following lines:

a

y = 7 x + 3

b

y = 3 x - 5

c

y = - 8 x - 3

d

y = - 8 x + 4

e

y = 9 x

f

y = 2

g

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

h

y = \dfrac {3 x + 8}{5}

6

Determine whether the following equations represent lines that will cross the y-axis at 2:

a

y = 5 x + 2

b

y = 2 - x

c

y = 2 x

d

y = 2 x - 4

e

y = x + 2

f

y = x - 2

g

y = 2

h

y = \dfrac{x + 4}{2}

7

The x-intercept occurs when y=0. Find the value of the x-intercept for the following lines:

a

y = 2 x - 2

b

3x + y = -3

c

y = 4 x - 8

d

2y + x = -3

e

y = 9 x

f

2y + 2x = 4

g

3x - 5y = 1

h

x = \dfrac {3 y + 10}{5}

8

For each of the following equations:

ii

Find the coordinates of the y-intercept.

i

Find the coordinates of the x-intercept.

iii

Use the intercepts to sketch the graph of the line.

a

y = 2 x - 4

b

y = - 2 x + 2

c

y = 3 x - 3

d

y = - 4 x + 8

Lines through the origin
9

Consider the linear equation y = 5 x .

a

Find the coordinates of the y-intercept.

b

Find the coordinates of the x-intercept.

c

Find the value of y when x = 2.

d

Hence, sketch the graph of the line.

10

Consider the linear equation y = - \dfrac {5 x}{4}.

a

Find the coordinates of the y-intercept.

b

Find the coordinates of the point on the line where x = 4.

c

Hence, sketch the graph of the line.

11

If a line has equation y=mx + c, explain how you can tell if the line will pass through the origin.

12

Determine whether the following equations represent lines that will pass through the origin:

a

y = 8 x - 8

b

y = \dfrac {x}{8}

c

y = - 6 x

d

y = 8 x

e

y = \dfrac {x}{8}

f

y = 0

g

y = - x

h

y = - 6 x - 6

Gradient
13

Consider the line graph shown:

a

State the y-value when x=0.

b

State the y-value when x=1.

c

When the x-value increases by 1, by how much does the y-value change?

d

Hence state the gradient of the line, m.

e

The equation of this line is y = 2 x + 4. Explain how to find the gradient from the equation of the line.

-4
-3
-2
-1
1
2
x
-2
-1
1
2
3
4
5
6
7
y
14

Consider the following three linear equations and their corresponding graphs:

y = 4 x + 3, \, y = 4 x + 6, \, y = 4 x - 3

a

What do all of the equations have in common?

b

What do all of the graphs have in common?

c

What conclusion can be made about lines that have the form y = 4 x + c?

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
15

Find the gradient, m, of the following linear equations:

a

y = 9 x + 3

b

y = - 7 x + 5

c

y = \dfrac{5x}{4} + 2

d

y = -x + 5

16

From the following list of equations, select the lines that have the same gradient:

  • y = 2 + 7 x

  • y = \dfrac {x}{7} + 2

  • y = 5 - 7 x

  • y = 7 x

  • y = 5 x + 7

  • y = 7 x - 2

17

For each linear equation:

i

Find the value, m, of the gradient.

ii

Find the value, c, of the y-intercept.

a

y = 2 x + 9

b

y = 5 x - 6

c

y = - 5 x + 8

d

y = - 4 x - 2

e

2y = 8 x - 1

f

3y = -6 x - 2

g

y - 5x = 4

h

2y - 3x = 6

18

Given the values of m and c, write the equation of the line:

a

m=2, c= 5

b

m=-3, c= 2

c

m=-2, c= -1

d

m=4, c= 0

e

m=0, c= -7

f

m=0, c= 4

g

m=\dfrac{1}{2}, c= -2

h

m=-\dfrac{3}{4}, c= \dfrac{1}{2}

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