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VCE 11 General 2023

3.03 Equation of a straight line

Worksheet
Equation of a line given the slope and y-intercept
1

State the equation of the following lines in slope-intercept form:

a

A line whose slope is - 8 and crosses the y-axis at - 9.

b

A line with slope - 3 and its y intercept is - 2.

c

A line which has a slope of \dfrac{3}{4}, and cuts the y -axis at - 1.

d

A line which has slope of \dfrac{2}{3} and goes through the point \left(0, 3\right).

e

A line that has the same slope as y = 7 - 3 x and the same y-intercept as y = -8 - 7 x .

2

State the equation of a line that goes through \left(0, \dfrac{2}{13}\right) and has a slope of 0.

3

For each of the following line graphs:

i

Find the slope.

ii

State the y-intercept.

iii

State the equation in slope-intercept form.

a
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
c
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
4

Find the equation of the following line in slope-intercept form:

-15
-12
-9
-6
-3
3
6
9
x
-10
-8
-6
-4
-2
2
4
6
8
10
y
5

Consider the following line graph:

a

State the y-intercept.

b

Find the slope.

c

Find the equation in slope-intercept form.

d

Rewrite the equation in general form.

-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
y
Equation of a line given the slope and a point
6

A straight line passes through the point \left(0,\dfrac{3}{4}\right) with slope 2.

a

Find the equation of the line in slope-intercept form.

b

Rewrite the equation in general form.

c

Find the x-intercept.

7

For each of the following lines:

i

Find y-intercept.

ii

Write the equation in slope-intercept form.

a

A line which has a slope of - 2 and passes through \left( - 6 , - 3 \right).

b

A line passes through Point A \left(8, 2\right) and has a slope of 2.

8

A line has slope - 2 and passes through the point \left( - 6 , - \dfrac{4}{3} \right).

a

Find the y-intercept.

b

Find the equation of the line in general form.

9

Given the following points and slopes, use the point-slope formula to express the equation of the line in slope-intercept form.

a

Point A \left( - 4 , 3\right), and slope - 9

b

Point A \left(8, 1\right), and slope \dfrac{5}{2}

c

Point A \left( - \dfrac{5}{9} , 7\right), and slope 7

d

Point A \left( - 4 , 5\right), and slope 3\dfrac{1}{2}

10

Consider the line with equation 2 x + y = 8.

a

Find the x-intercept of the line.

b

Find the equation of a line with a slope of - 4 that passes through the x-intercept of the original line.

Equation of a line given two points
11

For each of the following pairs of points:

i

Find the slope of the line that passes through the points.

ii

State the equation of this line.

a

\left(0, - 3 \right) and \left(1, 4\right)

b

\left(0, - 6 \right) and \left(6, - 48 \right)

c

\left(0, 4\right) and \left(2, 5\right)

d

\left(0, 3\right) and \left(4, 2\right)

e

\left(0, 1\right) and \left(3, 1\right)

f

\left(4, - 6 \right) and \left(6, - 9 \right)

g

\left( - 5 , 1\right) and \left(2, - 34 \right)

12

A line which goes through the points \left(0, 6\right) and \left(0, 8\right).

a

Find the slope of the line.

b

State the equation of the line.

13

Consider the line with equation 2 x - 3 y = -10.

a

Find the x-intercept of the line.

b

Find the equation of the line that passes through \left(7, 10\right) and the x-intercept of

2 x - 3 y = -10.

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Outcomes

U1.AoS4.1

the properties of linear functions and their graphs

U1.AoS4.3

the forms, rules, graphical images and tables for linear relations and equations

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