Download Unit 5 Linear Functions Summative Assessment

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Unit 5 Test
1. State if the equations below are linear or non-linear. If the equation is non-linear, explain
why.
a) y  2 x  1
b) 2 x  2 y  14
c) ( x  2) 2  6
d) y = |7𝑥 − 4|
2. Which of the following functions is non-linear? Please explain.
a)
b)
X
0
1
2
3
X
-1
Y
4
8
12
16
Y
-7
c)
0
-3
1
1
2
5
11
11
17
15
23
19
d)
X
Y
6
21
5
15
4
10
3
6
X
Y
5
7
3. If two triangles are similar(same angles, proportional sides, and different size), will they
have the same slope? Explain your answer.
1
𝑦 = − 2 𝑥 − 3 ? (MCC.8.EE.5)
b.
4. Which graph represents
y
a.
10
y
8
10
6
8
4
6
2
4
2
–8
–6
–4
–2
–2
2
4
6
x
8
–8
–4
–6
–4
–2
–2
–6
–4
–8
–6
–10
–8
2
4
6
8
x
2
4
6
8
x
–10
y
c.
–8
–6
–4
y
d.
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
x
8
–8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
5. Tara creates a budget for her weekly expenses. The graph shows how much money is in
the account at different times. Find the slope of the line and tell what the slope
represents in this specific scenario. (MCC.8.EE.5)
2750
2500
(4, 2400)
Amount ($)
2250
(12, 2000)
2000
1750
1500
1250
1000
750
500
250
2
4
6
8 10 12 14 16 18 20 22
Time (weeks)
a. 50; gain fifty dollars each week.
b. -50; decrease by fifty dollars each week.
c. 1/50; gain fifty dollars each week.
d. -1/50; decrease by fifty dollars each week.
6.
Does the table represent a linear or non-linear function? Explain. (MCC.8.F.3)
7.
What is the slope of the line that passes through the following points:
(4, 6) and (10, 2)
Graph the following functions. (MCC.8.EE.5)
8. y  2 x
9. y   x
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
x
𝟏
𝟏
𝒚 = 𝟐𝒙 + 𝟏
10.
11. 𝒚 = − 𝟐 𝒙 − 𝟏
y
y
5
5
4
4
3
3
2
2
1
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
–5
x
–4
–3
–2
–1
–1
1
x
5
x
–5
–5
12. y  x 2
13. y  4  x 2
y
y
14.
5
–4
–4
–3
4
–3
–3
–4
3
–2
–2
–5
2
–2
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
–5
x
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
Julio is training for a swimming race. The first part of his training schedule is shown.
(MCC.8.EE.5)
Session
Swimming distance (mi)
1
0.25
2
0.55
3
0.85
4
1.15
5
1.45
a. Is this training schedule a linear function? Explain why or why not.
b. How many miles will he be swimming on the 14th day?
6
1.75
15. The rate of change (slope) is constant in the graph. (MCC.8.EE.5)
600
Resale Value of a Refrigerator
Amounts ($)
500
400
300
200
100
3
6
9
12
15
18
Years after original purchase
a) Find the rate of change (slope).
b) Explain what the rate of change means for the situation.
Write the Equation for the Graphs Below
16.
17.
18. Compare the scenarios to determine which represents a greater speed. Include a description of
each scenario including the unit rates in your explanation. (MCC.8.EE.5)
Scenario 1:
Scenario 2:
y = 50x
x is time in hours
y is distance in miles
Label the graphs below as Positive, Negative, 0, or Undefined
19.
20.
21.
22.