Topics
7. Graphing Lines
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AustraliaQLD
Year 11

7.005 The gradient of a line

Lesson
Worksheet
Practice
Worksheet
Gradient from two points
1

For the following line segments AB:

i

State the rise from A to B.

ii

State the run from A to B.

iii

Hence find the gradient of line segment AB.

a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-4
-3
-2
-1
1
2
3
4
x
-3
-2
-1
1
2
3
4
5
y
2

Consider the following line, where A\left(4, 0\right) and B\left(1, 12\right) are both points on the line:

a

Find the gradient of the line.

b

As x increases, is the value of y increasing or decreasing?

-5
-4
-3
-2
-1
1
2
3
4
5
x
-16
-12
-8
-4
4
8
12
16
y
3

For the following graphs:

i

State the coordinates of the y-intercept.

ii

Find the rise from point A to the y-intercept.

iii

Find the run from point A to the y-intercept.

iv

Find the gradient of the line.

a
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
b
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
c
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
d
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
e
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
4

For each of the following linear equations:

i

Find the gradient of the line.

ii

State the coordinates of the y-intercept.

a

y = 5x + 6

b

y = - x - 8

c

y = 1 + 10 x

d

y = - 2 x

e

y = 24

f
y = - 1 - \dfrac{9 x}{2}
g
y = \dfrac{5 x}{6} - \dfrac{2}{3}
h
y = \dfrac{9 - 2 x}{4}
Gradient from a table of values
5

Consider the equation y = x and the table of values given below:

a

State the coordinates of the y-intercept.

b

As x increases, is the value of y increasing or decreasing?

c

Find the gradient of the line.

x- 3- 2-10
y- 3- 2-10
6

Consider the equation y = - x and the table of values given below:

a

State the coordinates of the y-intercept.

b

As x increases, is the value of y increasing or decreasing?

c

Find the gradient of the line.

x- 1012
y10-1- 2
7

Consider the equation y = 5 x and the table of values given below:

a

Find the coordinates of the y-intercept.

b

Find the gradient of the line.

x- 3- 2-10
y- 15- 10- 50
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