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Skill Builder

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1CHAPTER

Essential Review

Skill Builder: Introduction to Linear Functions 15

1 Introduction to Linear Functions REVIEW

1 State the rule of the following function.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

2 State the rule of the following relation.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

3 Determine if the following function has a direct or partial variation.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

4 Determine if the following function has a direct or partial variation.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

Skill Builder


16 Chapter 1: Essential Review

5 State the slope, y-intercept, domain and range of the following linear function.

2 3y x= +

6 State the slope, y-intercept, domain and range of the following linear function.

5y x= −

7 Find the zero (x-intercept) of the following linear function.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

8 Find the zero (x-intercept) of the following linear function.

3 12y x= − +

9 If a horizontal line passes through the point (3, 2), what is the rule for that line?

10 If a vertical line passes through the point (5, –7), what is the rule for that line?

Skill Builder


Skill Builder: Slope of a Line 17

1 Find the slope of the following function.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

(2,-3)

(8,6)


-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

(7,-6)

(2,4)


-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

(1,-3)

(4,6)


-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

(-5,-6)(5,-2)

2 Slope of a Line REVIEW

Skill Builder



5 Find the slope of the straight line between the following points.

( ) ( )1,6 and 6, 22A B− −

6 Find the slope of the straight line between the following points.

( ) ( )2,7 and 5, 8A B −

7 Show that the slope of the straight line between AB is the same as BA for the following points.

( ) ( )4,9 and 21, 91A B− −

8 Show that the slope of the straight line between AB is the same as BA for the following points.

( ) ( )12, 5 and 2, 23A B− −

9 Show that the following points are collinear by plotting the points on a graph and by finding the slope between the points.

( ) ( ) ( )6, 8 , 3, 5 and 9, 3A B C− − − −

10 Show that the following points are collinear by plotting the points on a graph and by finding the slope between the points.

( ) ( ) ( )8, 4 , 4, 3 and 4,1A B C− −

1 Find the rule of the following linear function in slope – intercept form.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

(7,-8)

(1,4)

2 Find the rule of the following linear function in slope – intercept form.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

(9,5)

(-6,-5)

3 Functional - Slope Intercept - Form of a Line REVIEW

Skill Builder


Skill Builder: General Form of a Line 19

3 Find the rule of the following linear function in slope – intercept form using the given coordinates. ( ) ( )1, 2 and 4,13− − −

4 Find the rule of the following linear function in slope – intercept form using the given coordinates. ( ) ( )3, 5 and 6, 2−

5 Find the rule of the following linear function in slope-intercept form that has a slope of 2 and passes through the point (–1, 4).

6 Find the rule of the following linear function in slope-intercept form that has a slope of –3 and passes through the point (2, –5).

7 Find the rule of the following linear function in slope-intercept form that has an initial value of 4 and passes through the point (2, 5).

8 Find the rule of the following linear function in slope-intercept form that has an initial value of 6 and passes through the point (–2, 0).

9 Find the rule of the following linear function in slope – intercept form using the given coordinates. ( ) ( )2, 5 and 3, 5−

10 Find the rule of the following linear function in slope – intercept form using the given coordinates. ( ) ( )4,6 and 2, 3− −

1 Find the rule of the following linear function in general form.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2 (6,0)(0,2)

2 Find the rule of the following linear function in general form.

-10 -8 -6 -4 -2 2 4 6 8 10-2

-4

-6

-8

-10

10

8

6

4

2

(9,5)

(-6,-5)

4 General Form of a Line REVIEW

Skill Builder



3 Find the rule of the following linear function in general form that has a slope of 2 and passes through the point (–1, 4).

4 Find the intercepts of the following linear function. 3 6 12 0x y− + =

5 Convert the following linear function into general form.

32

5y x= −


0.7 0.34y x= +


13 5

yx+ =


( )3 4 2y x+ = −

9 Convert the following linear function into slope – intercept form. 3 2 8 0x y+ − =

10 Convert the following linear function into

symmetric form 1yx

a b+ = where a is the

x-intercept and b is the y-intercept

4 5 40 0x y− − =

Hint: this question is just testing your algebra skills and your ability to find the intercepts in General Form, not your knowledge of “Symmetric Form”. Simply calculate the x-intercept and substitute it in for a, then calculate the y-intercept and substitute it in for b.

Skill Builder


Skill Builder: Graphing Linear Functions Level 2 21

5 Graphing Linear Functions Level 1 REVIEW

1 3 4y x= −

2 2

63

y x−

= +

3 6y x= −

4 4y x=

5 5y x= − +

6 3y x= +

7 64x

y = −

8 3

45

y x= − +

9 53x

y = − +

10 6y =

Graph the following linear functions using the y-intercept and the slope.

1 4 7y x= − +

2 2

65

y x= −

3 3

52

y x= − +

4 0.2 8y x= −

5 0.25 6y x= − +

6 2 3 12 0x y− − =

7 5 4 20x y+ =

8 4 2 0x y+ − =

9 8 5x y− =

10 2 3 8x y+ =

6 Graphing Linear Functions Level 2 REVIEW

Graph the following linear functions using a table of values.

Skill Builder



7 Solving Linear Equations REVIEW

1 4 5 3x − =

2 7 2 15x− =

3 3 4 19 2x x+ = −

4 ( ) ( )1 2 3 5x x x− + − = +

5 ( ) ( )3 6 1 4 3 2 2 3x x x− − + − = +

6 ( )5 10 2 7 2 4x x x+ = − + + −

7 ( ) ( )13 2 1 3 4x x x− − + = +

8 ( )2 5 2 3 9x x+ = − −

9 ( ) ( )3 1 2 4 5 6 1x x− − = − +

10 ( ) ( )4 3 2 2 3x x x x− − = − −

Solve for x.

1 In a class of 20 students, there are 4 more boys than girls. How many girls are in the class? How many boys are in the class?

2 Today, Billy is 2 years older than Sally. In 5 years the sum of their ages will be equal to 40 years. How old are Billy and Sally today?

3 What two consecutive even integers add up to 70?

4 Two-thirds of a certain number is 3 more than one-half of the number. What is this number?

5 The length of a rectangle is 5 more than its width. The perimeter of the rectangle is 70 cm. What are the length and width?

6 The sum of three numbers is –7. The second number is 6 more than the first; the third number is 11 more than the first. What are the three numbers?

7 The area of a triangle is 60 squared meters. If its base is 12 m, what is the height of the triangle?

8 Billy has $24.00 in his not so manly men’s European hand bag. The money is in quarters, $1’s and $2’s. He has 2 fewer $2’s than $1’s, and twice as many quarters as $1’s. How many quarters, $1’s, and $2’s does Billy have?

9 Billy leaves Montreal at 6 am to go to Toronto and travels at an average speed of 60km/hr. One hour later, Sally leaves from the same place at an average speed of 100km/hr toward Toronto too. At what time and distance does Sally reach Billy?

10 Sally pays $5 for 4 apples and 3 oranges. If an orange costs 15 cents more than an apple, how much would Sally pay for 5 apples and 2 oranges?

8 Solving First Degree Word Problems REVIEW

Skill Builder


Skill Builder: An Introduction to Inequalities 23

1 Write the following statement as an inequality.

The minimum value of x is 13.


X is greater than or equal to zero.


X is less than or equal to 9.


X is greater than 5.


X can be no more than 7.

6 Translate the following statement into an inequality. Let x represent the number teams in a basketball tournament. There are at most, 16 teams in a basketball tournament.

7 Translate the following statement into an inequality. Let x represent the number of snow-boarders at Mont Orford last Saturday. There were at least 300 snow-boarders at Mont Orford.

8 Translate the following statement into an inequality. Let x represent the number of girls in a Math class. There is a maximum of 18 girls in that Math class.

9 Jamel is a car salesman. He earns a weekly base salary of $300 and a bonus of $500 for every car he sells. If x represents the number of cars he sold last week, what inequality describes him earning a total salary of less than $2500?

10 At a day camp there are 15 more boys than girls. Let x be the number of girls at the camp. What inequality would describe the situation where there are more than 150 campers and a maximum of 200 campers?

9 An Introduction to Inequalities REVIEW

Skill Builder



1 Solve the following inequality. 11x + 3 > 30−

2 Solve the following inequality. 4x + 3 27≥

3 Solve the following inequality. -2x 5 < -x + 3−

4 Solve the following inequality. ( )-2 x + 1 6≥ −

5 Solve the following inequality and give the solution set in interval notation. 2x 4

83−

≤

6 Solve the following inequality and give the solution set in interval notation. -3x + 2 < -10

7 Solve the following inequality and give the solution set in interval notation.

( ) ( )5 x 1 6 x + 1 > 0− −

8 Solve the following inequality and give the solution set in interval notation. -7 -3x + 2 -1≤ ≤

9 The width of Duane’s rectangular property measures 15 m less than twice the length. If the perimeter is at least 120 m, what is the minimum length of Duane’s property?

10 In Bermuda, a scooter rental company charges an initial fee of $1.25 and then $0.75 per km travelled. In what interval is the distance travelled if the cost of the rental is more than $11 but less than $14?

10 Solving One-Variable First Degree Inequalities REVIEW

Skill Builder


Skill Builder: Solving Linear Systems by Graphing 25

11 Graphing Linear Inequalities REVIEW

1 x ≥ 2

2 x < 3

3 y ≥ 2

4 y < 6

5 y ≤ x + 2

6 y > 2x – 4

7 5x + 2y < 20

8 2x + 3y – 6 ≥ 0

9 x > 1 y < 7

10 x < 6 y ≥ 0

Graph the solution set for the following inequalities.

1 53

2

y x

y x

= −

−=

2 2 61

42

y x

y x

= −

−= +

3 42 8x y

x y

− = − =

4 3 4 1210

x y

x y

− = + = −

5 2 82 5 20y x

x y

= − + =

6 3 64 28

y x

x y

= − + − =

7 ( )2 3 1

15

3

y x

y x

+ = − −

= +

8 ( )14 6

28

y x

x y

− − = + − =

9 2 53 1

y x

y x

= − = − +

10 2 3 182 8

x y

x y

+ = − =

12 Solving Linear Systems by Graphing EVALUATED

Find the solution to the following systems of linear equations by graphing.

Skill Builder



1 Solve the system of equations using a graph:

2x yy x

− = − = −

2 Solve the system of equations using a graph:

2 57

y xy x+ =

− = −

3 Solve by substitution using Algebra Tiles:

62

y xx y

− = + =

4 Solve by substitution using Algebra Tiles:

2 62

y xy x− =

− = −

5 Solve by substitution using Algebra:

5 55

y xy x− =

− =

6 Solve by substitution using Algebra:

2 3 32 7

x yy x

+ = = −

7 Solve by comparison using a Balance Model and Algebra:

2 25

y xy x

= + = − +

13 Modeling Systems of Linear Equations REVIEW

Skill Builder


Skill Builder: Modeling Systems of Linear Equations 27

8 Solve by comparison using a Balance Model and Algebra:

3 22 8

y xy x

= − + = −

9 Solve by elimination using Algebra and Algebra Tiles:

3 2 52 9

x yx y

− = − + =

10 Solve by elimination using Algebra and Algebra Tiles:

2 11

y xx y

− = − − = −

Skill Builder



3 56 17

y x

y x

= − = −

2 32 8

y x

y x

= − = −

3 4 1410 2

y x

y x

= + = +

4 37 6

y x

y x

= = −

5 22 12

x y

x y

= − = −

6 2 82 2 34

x y

x y

= − = − +

7 2 283 72y x

x y

= − + =

8 3 26 2 20y x

x y

= − + =

9 Alpha Motocross charges a one-time membership fee of $210 and $20 every time you ride. Beta Racing charges $35 every time you ride, but only charges $105 for their membership.

How many times would you have to ride at each for the total cost to be the same?

10 Bart and Betty each go out babysitting on Friday night. Bart gets paid $9 per hour and receives a tip of $15 at the end of the night. Betty gets paid $10 per hour and receives a tip of $9.

If they each made the same amount, then how many hours did they work and how much money did they earn?

1

14 Comparison Method REVIEW

Find the solution to the following systems of equations using the comparison method.

Skill Builder


Skill Builder: Substitution Method 29

1 2 32 3 7y x

x y

= − − = −

2 2 52 5 9y x

x y

= − − =

3 3 12 3 3x y

x y

= + − =

4 2 103 5 3x y

x y

= + + = −

5 5 302 3 25

x y

x y

+ = + =

6 3 57 6 20x y

x y

+ = + =

7 2 8 417 31 3

x y

x y

= − − =

8 3 6 215 2 4

y x

x y

= − + + =

9 Joe is 10 years older than three times his son’s age. The sum of their ages is 58. How old are Joe and his son?

10 The length of a rectangle is 5 units more than twice its width. The perimeter of this rectangle is 220 units. What is the area of this rectangle?

15 Substitution Method REVIEW

Find the solution to the following systems of linear equations by using the substitution method.

Skill Builder



1 Find the solution to the following system of linear equations by using the elimination method.

2 3 132 4

x y

x y

+ = − = −


5 8 293 6 21

x y

x y

+ = + =


3 2 54 10

x y

x y

− + = − =

4 Find the solution to the following system of linear equations by using the subtraction method.

3 4 16 3 13

x y

x y

− = + =


3 5 92 1

x y

x y

+ = + = −


5 3 33 2 1

x y

x y

+ = − + = −

7 Find the solution to the following system of linear equations by using the addition method.

3 2 16 4 10

x y

x y

+ = − − =

8 Find the solution to the following system of linear equations by using the addition method.

3 10 25 1

x y

x y

− + = − =

9 The perimeter of a rectangle is equal to 60cm. If the length is doubled and the width is tripled, then the perimeter of the new rectangle is 144cm. What was the original length and width?

10 Jen buys two sweaters and three shirts for $220. Tina buys three sweaters and two shirts for $230 in the same store. If all the sweaters are the same price, and all the shirts are the same price (but different from the sweaters), how much will it cost to buy four sweaters and two shirts?

16 Elimination Method REVIEW

math - chapter essential review 1mrdesuamath.weebly.com/uploads/1/1/0/9/11093857/sec_5... · 2018....

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