MPM 1DT – Assignment
Linear Relations
Name: ______________________________
Part A – Answer in the space provided. Each correct answer is worth one mark. (22 marks)
1. What is the slope given the equation y = -x + 4
____________
2. The letter b in the equation y  mx  b represents the
3. State the slope of a horizontal line
slope / y intercept
(circle one)
____________
4. Which equation best matches the following data in the table?
____________
x
0
1
2
Y
10
15
20
a) y = 10x + 5
b) y = -10x + 5
c) y = 5x +10
5. Which of the following slopes is the steepest ?
[2]
____________
6
d) m  5
5
Fill in the missing information, given the equation of the line is y = 3x - 7.
a) m  4
6.
d) y = -5x +10
b) m  3
x
0
1
c) m 
Y
0
2
7. A line has an equation 15 x  3 y  30  0 :
i) State the slope of this line.
____________
ii) State the y intercept of this line.
____________
iii) The x intercept of this line is
____________
8. In the equation y = 0.75x , the slope is
____________
the y-intercept is
____________
9. Do the lines y  2 x  3 and y  2 x  4 intersect?
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YES / NO
(circle one)
10. Use the graph below to answer the following questions:
i.
What is the slope of the line that passes through points A and B?
____________
ii.
Which point is the y intercept?
____________
iii.
Write D as an ordered pair
____________
iv.
Plot the point F(-4,3) on the grid below.
11. Give an equation of a line which is parallel
to y = -5x – 4 and has a y-intercept of –2:
____________
12. Is the equation in the previous question (question 11)
an example of direct or partial variation?
direct / partial
(circle one)
13. The point (0, -6) is a special point called the x intercept.
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True / False
(circle one)
Part B – Answer in the space provided (32 marks).
14. Complete the table of values for the line y = –2x – 3 and then graph the line. (3 marks)
x
y = –2x – 3
0
1
-1
-2
-3
15. Graph y 
1
x  1 on the above graph using the slope, y- intercept method (2 marks)
2
1
(2 marks)
3
b) Write the equation of the line at the
left in the form y = mx + b. (2 marks)
16. a) Graph the line that passes through the point (–3, –2) and has a slope of
17. On the above graph, graph the lines y = -2 and x = 4 (label these lines). (2 marks)
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18. The cost of a health club membership is based on a one-time membership fee plus a monthly
user fee rate. The following table shows the cost for a six month membership and a ten month
membership. The cost includes both the initiation fee and the monthly fees.
Time (# of months)
Cost (dollars)
3 months
$200
7 months
$500
a. Find the monthly user fee rate (you may use the grid to assist you). (3 marks)
y
x
b. Find the one-time membership fee.
(2 marks)
c) Write an algebraic model that represents
the total cost of this membership? (1 mark)
c. Using your algebraic model to find the cost of a 2-year membership. (2 marks)
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19. Graph the line 7 x  14 y  28  0 . Show your work when determining these intercepts.
(4 marks)
20. Find the equation of the line that passes through (–6, 1) and (3, –2). (5 marks)
21. Write the equation of the line that is parallel to y 
(6, -1). (4 marks)
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2
x  2 and passes through the point
5
22. Janine lives 600m from the Video Shoppe. She stopped and talked to a friend for 3 minutes on
her way to the store. Then she ran to the store before it closed. She walked home. Which
graph best describes her trip?
__________________
600
(b)
600
400
Distance [m]
Distance [m]
(a)
200
0
0
10
2
4
6
400
200
0
8
0
10
2
Time [min]
4
6
8
Time [min]
(d)
600
600
400
400
Distance [m]
Distance [m]
(c)
200
0
0
10
2
4
6
8
200
0
0
10
Time [min]
2
4
6
8
Time [min]
23. This graph models how the height of water in a container being filled changes over time.
Select the container that is probably being filled.
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Make a graph with at least 3 different slopes. Calculate the slope (speed) of each section.
Include specific distances and time lengths as well as specific starting and ending points.
Write a story that includes the information from the graph (distances, times, speeds).
Graph
Distance in __________
Title: ___________________________
Time in _____________
Story
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