Thinking Questions/EQAO Practice – Slope Name:__________________
1.
2.
3.
4.
5.
For each graph, state the following.
a)
slope _________________
y-intercept _____________
equation of line _____________
equation of line ______________
10
10
8
8
6
6
4
4
2
2
2
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8 10
Find the slope of the line passing through the following points.
a) (4, 0) and (-5, -6)
7.
slope __________________
y-intercept _____________
-10 -8 -6 -4 -2
6.
b)
b) (-3, 8) and (-5, -6)
Graph the following lines using the method indicated.
2
x4
3
Slope y-intercept method
a) y  
b) 2x + y = 4
x- and y-intercepts method (show work on the side)
x
y
8.
Complete the following chart.
Equation
y
Slope
y-intercept
3
x 1
5
2
Slope of a line
parallel
Slope of a line
perpendicular
1
4
y=2
9.
Find the equation of the line passing through the point (-3, 1) with a slope of 4. Put the
final answer in slope y-intercept form.
10.
Find the equation of the line passing through the two points (-1,2) and (3, 5).
11.
Find the point of intersection of the two lines by graphing the lines.
y  2x  1
1
y x9
2
12.
Write an equation of a line parallel to y =
2
x + 5 that has the same y-intercept as
3
y = 4x -7
13.
Find the equation of the line that is parallel to -4x +3y -24 = 0 that passes through the
point (-2, -6). Write the equation in standard form.
14.
Find the equation of the line that is perpindicular to -4x +3y -24 = 0 that passes through
the point (-2, -6). Write the equation in standard form.
15.
Find the equation of the line that is perpindicular to 6x +4y -48 = 0 that passes through
the y – intercept of the line defined by -8x +2y -32 = 0. Write the equation in standard
form.
16.
Find the equation of the line that is perpindicular to 6x +4y -48 = 0 that passes through
the x – intercept of the line defined by -8x +2y -32 = 0. Write the equation in standard
form.
17.
Find the equation of the line that is perpindicular to 3x +2y -8 = 0 that passes through
the y – intercept of the line defined by -x +2y -12 = 0. Write the equation in standard
form.
18.
Write the equation for each relationship in the space provided. Show any calculations
you made. Indicate if the relation is a partial or direct variation and whether the line
modelling the relationship is solid or dashed.
A coaches B
a. Rent a car for the weekend costs $50
plus $0.16/km.
B coaches A
b. A race car travels at a constant speed of
220km/h. Write an equation for the total
distance travelled over time.
c.
d.
e.
Distance
(km)
0
10
20
30
40
Cost of a Taxi
Fare ($)
3.50
6.50
9.50
12.50
15.50
f.
Distance
(km)
0
100
200
300
400
Cost of Bus
Charter ($)
170
210
250
290
330
19.
Determine the first differences of the relation and state if the relation is
linear or non-linear.
x
0
1
2
3
4
20.
y
0
2
5
9
14
First differences
The table of values represents a direct variation. Determine the rate of change
“m” and use it to complete the following table of values.
x
-1
-2
2
6
8
10
21.
y
8
-32
Determine the rate of change of the following graph.
a) $5 / hr
c) $16.67 / hr
Money Earned ($)
b) $10 / hr
50
a) $20 / hr
40
30
20
10
0
0
1
2
3
4
5
6
Hours Worked
Determine the equation of the following graph. Let M be the money earned and
16
h be the time in hours.
b) M = 1h + 4
c) M = 2h + 4
d) M = 2.8h + 4
Money Earned ($)
22.
14
12
10
8
6
4
2
0
0
e) M = – 2.8h + 14
1
2
3
4
Hours Worked
8
5
23.
An amusement park charges $10.00 admission and $1.25 per ride. Determine
the equation representing the cost of a trip to the park, where r is the number of
rides and C is the cost.
a) C = 1.25r + 10
b) C = – 1.25r + 10
c) C = 10r + 1.25
d) C = – 10r + 1.25
24.
25.
The slope of a line perpendicular to the line y = 3x - 7 is:
1
1
a)
b) c) 3
3
3
d) -3
The slope of a vertical line is:
a) m = 0
b) m = undefined
c) m = 1
d) m = -1
26.
Determine the slope and the y-intercept of the line passing through the points A
(5, 4) and B (3, 8).
27.
Determine the equation of a line that passes through the point (-4, -10) with a
slope of 5.
9
28.
Determine the slope and y-intercept for the line represented by the following
table.
X
y
-5
-2
1
4
7
17
11
5
-1
-7
29.
Write the equation y = 4x – 5 in standard form.
30.
Write the equation 2x – 3y + 7 = 0 in slope y-intercept form.
31.
The Halton District School Board decided that every high school must have a
minimum of 30 recycling bins. For high schools with an enrollment above 800
students, the school must add 1 additional recycling bin for each increase of 100
students over the 800 mark. The graph is shown below.
# of recycling boxes
Explain how the graph would change if the
Board decided that schools with an enrollment
above 800 students would add 2 additional
recycling bins for each increase of 100 students
# of bins
over the 800 mark. Draw a sketch of the new
line on the given graph.
Population
10
32.
The yearbook club at Abbey Park is looking into the costs of the yearbook. A
representative from Josten’s tells them that the cost will be $12 300 for 1200
yearbooks and $15 000 for 1500 yearbooks. Determine an equation to represent
the cost of yearbooks (C) in terms of the number of yearbooks purchased (n).
33.
Determine the slope and y-intercept of the line 2x – 5y = 15.
34.
Determine the x and y-intercepts for the line 2x – 3y = 6 and graph the line on
the given grid.
35.
Determine the equation of a line that is parallel to the line y =
1
x – 1 and passes
3
through the point P(2, 7).
11
36.
Determine the equation of a line that is perpendicular to the line y = -2x + 7 with
an x-intercept of 4.
37.
12