MFM 2P Linear Relations Exam Review Name:

Skill #1: Points on the Cartesian plane

1) Complete the following question by stating the coordinates of the points on the Cartesian plane and plotting the points listed below. (6 marks)

Plot the following points on the:

A (2, 3)

B (-4, -2)

C (-3, 5)

State the coordinates of the following points:

D:

E:

F:

Skill #2: Slope and y-intercept

1) Define the following terms in your own words: (2 marks)

Slope:

y-intercept:

2) For each of the following graphs, state the slope and y-intercept: 8 marks

a) Slope: ___________________

y-intercept:____________

b)

Slope: ___________________

y-intercept:____________

c) Slope: ___________________

y-intercept:____________

d) Slope: ___________________

y-intercept:____________

Skill #3: Properties of Slope1) For the following, whether the equation of the line has a positive, negative or

zero slope. Then state the slope, y-intercept and equation of a parallel line and graph the line.

2)a) y = 2x + 4

____________________

i. Slope: ________________

ii. y-int: _________________

iii. Equation of a parallel line: ____________

b) y = -1/3x -7 ________________

i. Slope: ________________

ii. y-int: _________________

iii. Equation of a parallel line:______________

c) y = 5___________________

i. Slope: ________________

ii. y-int: _________________

iii. Equation of a parallel line:_________________

d)

i. Slope: ________________

ii. y-int: _________________

iii. Equation of a parallel line P:________________

Skill # 4: Table of ValuesFor the following use the table of values to determine the equation of the line or use the equation of the line to complete the table of values and determine the rate of change. (5 marks)

a) Equation: ____________________ b) y = -1/3x + 5

X Y Rate of Change

-1 2

0 0

1 -2

2 -4

3 -6

X Y Rate of Change

Skill #5: Determining the Equation of a Line problemsFor the following questions you can find the answer by graphing or creating a table of values.

1) Determine the equation of a line that has a slope of -2 and passes through point (3,-5) (5 marks)

2) Determine the equation of a line that passes through points (-3, 5) and (2, 7). (5 marks)

3) Mr. Doble’s basic cell plan charges $15 each month and an additional $0.02 per text message sent. (5 marks)

a. Determine the equation of the line that would represent this plan.

b. What would Mr. Doble’s plan cost her if he sent 200 text messages in a month?

Skill #6: Solving Equations:1) Solve the following equations: (1 mark each)

a. x + 4 = 12 b. 2x + 5 = 7

c. -7k = 28 d. 8 – t = 10

e. 3d – 1 = 8

2) Solve the following equations: (2 marks each)

a. 3t+42

=5 b. 1.25k + 0.75 = 0.5k

c. 6(x – 2) = 3x d. 3(y + 1) = 2(y – 3)

e. x+63

=2+ x−25

3) For the following equations:a. Describe the operations that are affecting acting on the variableb. List the steps required to undo the operations

i. 4x = 36 (2 marks) ii. w+46

=3

Skill #7: Solving for the slope and y-intercept1) Rearrange the following equations to get y = mx + b form. Then state the

slope and y-intercept. (16 marks)a. 2x + y -3 = 0 b. 6x – y – 1 = 0

Slope= Slope = y-intercept = y-intercept =

c. 2x + 3y – 12 = 0 d. 4x – 5y + 10 = 0

Slope= Slope = y-intercept = y-intercept =

2. Use the information from the graphs below to determine the slope and y-intercept for each line. (4 marks)a. b.

Slope= Slope = y-intercept = y-intercept =

Skill #8: Application of equations1) The total cost of a meal at a banquet hall is $20 per person, plus a $500

charge for renting the hall.a. If there is a $500 charge for renting the hall itself, write an equation

for the cost of booking the hall and state the slope and y-intercept of the line. (3 marks)

b. Find the total cost for 60 guests. (1 mark)

c. Suppose the total cost war $2160. Find the number of guests. (1 mark)

2) Masani is testing 25g of fertilizer. She plans to give each plant 0.4g of the fertilizer and have 8g left over for future tests. How many plants can Masani use in her tests given the equation 0.4n + 8 = 25. (2 marks)

Skill #9: Determining Point of Intersection by Graphing

1) Solve the following system by graphing the two lines on the graph provided and determining the point of intersection. (You must graph the lines to get full marks) (3 marks each)

a. y = 2x + 3 a. y = -x + 3b. y = x + 4 b. y = 3x - 5

Point of Intersection: Point of Intersection:

a. y = 2x + 6 a. y = -13x + 3

b. y = 12x b. y = 2x - 4

Point of Intersection: Point of Intersection:

2) Use Desmos to determine the point of intersection of the following systems of equations: (1 mark each)

a. y = 7x + 1 b. 2x + y = 42x + y = 10 4x – y = -1

c. y = 5x - 6 d. y = -4x + 23

y = 25x - 35 2x – y + 83= 0

Skill #10: Determining the Point of Intersection by Substitution or Elimination

3) Solve the following systems of linear equations using either the substitution method or solving by elimination. (You can check your answer with Desmos, but I need to see your solution for full marks) (3 marks each)

a. 3x + 2y - 1= 0 #1 b. 3x – y = 4 #1y = -x + 3 #2 x + y = 8 #2

c. x + 4y = 5 #1 d. 2x + y =3 #1x + 2y = 7 #2 4x – 3y = 1 #2

e. 2x + 3y = -1 #1 f. x – 3y = -2 #1x + y = 1 #2 2x + 5y = 7 #2

g. 6x + 5y = 7 #1 h. x – 3y = 5 #1x – y = 3 #2 7x + 2y = 12 #2

Skill #11: Word Problems involving Point of Intersection

Word Problems: For each of the following questions you can use any strategy that you prefer to find the final answer (graphing, substitution or elimination). Each question will be assessed out of 5 marks.

4) Isabella rode her motorcycle at a constant speed. It took her 2 hours to travel 216km with the wind behind her. The return trip took 3 hours riding into the wind.

a. Let s represent the speed of the motorcycle and w represent the speed of the wind. Write a linear system to represent this situation.

b. Find the speed of the motorcycle and the speed of the wind.

5) Anna has a total of $6000 to invest. She puts part of it in an investment paying 8% per year, and the rest in an investment paying 6% per year. At the end of one year, Anna earned $440 in interest. How much did she invest at each rate?

6) Carlie has a jar of coins. She tells her sister that the jar has 45 quarters and dimes altogether and the value of the coins is $6.30. Find the number of each type of coin in the jar.