Mathematics 9 – ES Laird
Unit #2 – Patterns and Relations
Quiz #2 – Graphing - Review
1. In each equation, determine the value of R when t = 2
a. 𝑅 = 𝑡 − 5 R = -3
c. 𝑅 = 4𝑡 + 1 R = 9
b. 𝑅 = −2𝑡 + 2 R = -2
d. 𝑅 = −3𝑡 − 2R = -8
2. The pattern in the table of values below continues. Which equation correctly relates
“x” to “y”?
a. 𝑦 = 3𝑥 + 9
X
Y
1
6
b. 𝑦 = −3𝑥 − 9
2
3
c. 𝑦 = 3𝑥 − 9
3
0
d. 𝑦 = −3𝑥 + 9
4
-3
3. Make a table of values for each relation. Use values of “x” from -2 to 2.
a. 3𝑥 + 𝑦 = 2
b. 2𝑥 − 𝑦 = 4
X
Y
X
Y
-2
8
-2
-8
-1
5
-1
-6
0
2
0
-4
1
-1
1
-2
2
-4
2
0
4. Graph the following using a table of values.
a. 𝑦 = −2𝑥
b. 𝑦 = 2 − 4𝑥
5. Graph the following using the slope-intercept method.
5
b. 𝑦 = −3𝑥 + 2
a. 𝑦 = 2 𝑥 + 3
6. For each equation indicate whether it would describe a vertical line, a horizontal line or
an oblique line.
a. 𝑦 = 7 Horizontal Line
d. 𝑥 = −2 Vertical Line
b. 3𝑦 = 7𝑥 Oblique Line
e. 𝑥 = 0 Vertical Line
c. 3𝑦 = 7𝑥 − 5 Oblique Line
f. 𝑦 = 43 Horizontal Line
7. Indicate whether the table of values describes an increasing function, decreasing
function or neither along with how you know.
a.
b.
c.
X
1
2
3
4
Y
5
7
9
11
X
-3
0
3
6
Y
5
0
-5
-10
X
-4
-2
0
2
a) Increasing because as x increases in value y does as well.
b) Decreasing because as x increases in value y decreases.
c) Increasing because as x increases in value y does as well.
Y
-6
-5
-4
-3
8. Determine if each of the table of values represents a linear relation; Explain your reasoning.
a) Linear because there is a
constant common difference
between terms
X
1
3
5
7
Y
6
9
12
15
b) Not Linear because there
is no constant common
difference between terms.
c) Not Linear because there
is no constant common
difference between terms.
X
2
0
2
4
X
3
5
7
9
Y
9
4
-2
-9
Y
8
9
12
17
9. Explain how you can tell if (a) a graph, (b) a table of values, and (c) an equation is linear or non-linear.
a) A graph is linear if it is a straight line, any curvy lines are not linear.
b) A table of values is linear if there is a constant common difference between terms; any terms without
a common difference indicates a non-linear function.
c) An Equation is linear if there is an x, or a y, or both an x and a y variable that is raised to the degree
one. If there are three or more variables, or any degree is different than 1 then it is a non-linear
function.
10. If the table of values below represents a linear relation, fill in the blanks correctly.
a)
X
-2
0
2
4
b)
Y
7
5
3
1
X
1
2
3
4
c)
Y
3
7
11
15
X
4
2
0
-2
Y
7
13
19
25
11. Determine an equation for each of the tables of values.
a) 𝑦 = −3𝑥 + 1
X
-2
-1
0
1
Y
7
4
1
-2
5
b) 𝑦 = 2 𝑥
c) 𝑦 = 𝑥 + 1
d) 𝑦 = −4𝑥 − 13
X
2
4
6
8
X
7
6
5
4
X
-4
-2
0
2
Y
5
10
15
20
Y
8
7
6
5
Y
3
-5
-13
-21
12. A phone company charges a base monthly fee of $25 and an additional $0.30 for every minute of
airtime used. Let C be the monthly cost of a bill and n be the number of minutes of airtime used.
a) Write an equation that relates C to n 𝐶 = 0.30𝑛 + 25
b) Create a table of values to represent this situation. Use realistic numbers.
N
C
0
25
30
34
60
43
90
52
c) Determine the bill for a person who talked for 3 hours of air time. $79 bill
13. The difference of two integers is 9. Let x be the larger integer and y represent the smaller integer.
a) Write an equation relating x and y. 𝑥 − 𝑦 = 9
b) Create a table of values for 5 different values of x.
**Any numbers would work**
X
Y
11
2
10
1
9
0
8
-1
7
-2
14. Maya jogs on a running track. The graph shows how far she jogs in 10 minutes. Assume Maya
continues to jog at the same average speed. Use the graph to
a) Between 16 and 17 minutes
b) Between 1600 and 1700 meters
c) I assumed that Maya continued to jog at the same rate.
15. Answers will vary
b) you should be able to connect the points
c) answers will vary between $1.15 to $1.25
d) approximately 300-350 mL
16. a) i) x = -1 ii) x = 5
iii) x = 7
b) i) y = -1
ii) y = 4
iii) y - 7
17. Calculate the value of x if y = -2 in each of the following equations.
a) y - 3 = 2x x = 2.5
b) -3x + 2y = 9 x = -13/3 = 4.3333
c) y = x – 5 x = 3
d) 2x = 12 + y x = 25
e) 2x + 3y = 4 x = 5
f) x = 2y – 1 x = -5