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CanadaON
Grade 9

6.06 Slope-intercept form

Worksheet
Slopes and y-intercepts
1

Consider the following graphs of the equations y = x + 3, y = 2 x + 3 and \\y = 4 x + 3:

a

What is the same about all three equations?

b

What is the same about all three lines?

c

What can be concluded about the constants in equations and the \\y-intercepts of their graphs?

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

What does the following stand for in the equation of a line: y = ax + b?

a
a
b
b
3

State the y-intercept of the line y = - x + 6.

4

For each of the following equations:

i

State the y-intercept.

ii

State the slope.

a
y = 7x - 8
b
y = -x + 5
c
y = -9x-3
d
y = 4 + 9x
e
y = -2x
f
y = - 1 - \dfrac{9 x}{2}
g
y = \dfrac{x-4}{5}
h
y = \dfrac{11 - 2x}{3}
5

For each of the following lines:

i

State the y-intercept.

ii

Find the slope.

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
-4
-3
-2
-1
1
2
3
4
y
c
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
d
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
e
-4
-3
-2
-1
1
2
3
4
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
y
f
-3
-2
-1
1
2
3
x
-4
-3
-2
-1
1
2
3
4
5
6
y
Equation from a line
6

For each of the following lines:

i

State the slope.

ii

State the y-intercept.

iii

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

a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
c
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
d
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
e
-4
-3
-2
-1
1
2
3
4
x
-1
1
2
3
4
5
6
7
y
f
-4
-3
-2
-1
1
2
3
4
x
-35
-30
-25
-20
-15
-10
-5
y
g
-4
-3
-2
-1
1
2
3
4
x
-7
-6
-5
-4
-3
-2
-1
1
y
h
2
4
6
8
10
12
14
16
x
-1
1
2
3
4
5
6
7
y
i
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
5
y
j
-4
-3
-2
-1
1
2
3
4
x
-1
1
2
3
4
5
6
7
y
7

Find the equation of the following lines:

a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-16
-14
-12
-10
-8
-6
-4
-2
x
-7
-6
-5
-4
-3
-2
-1
1
y
8

Consider the following table of values:

x-2024
y6420
a

Graph the line going through these points.

b

Write the equation of the line that goes through these points.

9

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

a

A line that has a slope of - 3 and crosses the y-axis at 1.

b

A line that has a slope of 2 and a y-intercept of - 5.

c

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

d

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

e

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

Graph of a line from an equation
10

Sketch the graph of a line with y-intercept of - 2 and slope of 5.

11

Sketch the graph of the following linear equations:

a

y = - 4 x + 4

b

y = 2 x-1

c

y = 4 x + 3

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

y = 4 x - 1

12

Determine whether the following lines pass through the origin \left(0 , 0\right):

a

y = 6 x

b

y = \dfrac{x}{6}

c

y = 6 x - 6

d

y = 8 x + 8

e

y = 8 x

Equations of horizontal and vertical lines
13

State the equation of the following graphed lines:

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

Sketch the following lines on a number plane:

a
x = 2
b
x = -8
c
y = 1
d
y = -7
15

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

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

x 4.5 0.5 3.5 8.5
y 0 0 0 0
16

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
17

State the point of intersection of the following pairs of lines:

a

x = 6 and y = - 3

b

x = 1 and y = 5

c

x = -2 and y = - 1

d

x = 0 and y = 8

Applications
18

A cleaner charges a callout fee of \$90 plus \$30 per hour.

a

Write an equation to represent the total amount charged, y, by the cleaner as a function of the number of hours worked, x.

b

Sketch the graph of y against x for 0 \leq x \leq 6.

c

State the slope of the line.

d

State the y-intercept.

19

Robert is running a 80 \text{ km} ultramarathon at an average speed of 15 \text{ km/h}.

a

Write an equation to represent the distance Robert has left to run, y, as a function of the number of hours since the start, x.

b

Sketch the graph of y against x for 0 \leq x \leq 6.

c

State the slope of the line.

d

State the y-intercept.

20

Mario is running a 100 \text{ km} ultramarathon at an average speed of 9 \text{ km/h}.

a

Write an equation to represent the distance Mario has left to run, y, as a function of the number of hours since the start, x.

b

State the slope of the function.

c

Describe what the slope of the line represents in context.

d

State the y-intercept.

e

Describe what the y-intercept represents in context.

f

Find the distance Mario will have left to run after 4.5 hours.

21

The cost of a taxi ride is given by C = 4.5 t + 9, where t is the duration of a trip in minutes.

a

Find the cost of an 11-minute trip.

b

For every extra minute the trip takes, how much more will the trip cost?

22

Harry currently gets no base salary, but earns \$60 per house for cleaning houses. His contract is updated and he will now get a guaranteed base salary of \$500 per week, but will earn \$40 less per house.

Write an equation to represent the relationship between number of houses cleaned, h, and weekly wage, W.

23

Jim's Gym offers a membership that can be modelled by the equation C = 100 + 13 n. Where C is the total cost and n is the number of weeks.

What does 100 and 13 in the formula mean in this context?

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Outcomes

9.B3.4

Solve problems involving operations with positive and negative fractions and mixed numbers, including problems involving formulas, measurements, and linear relations, using technology when appropriate.

9.C3.1

Compare the shapes of graphs of linear and non-linear relations to describe their rates of change, to make connections to growing and shrinking patterns, and to make predictions.

9.C3.2

Represent linear relations using concrete materials, tables of values, graphs, and equations, and make connections between the various representations to demonstrate an understanding of rates of change and initial values.

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