SDUHSD Math B Honors Module #2 – TEACHER EDITION 2016-2017
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2.2E Homework: Deriving the equations y = mx and y = mx + b *
Name: Period:
1. Fill in the blanks using the words proportional or linear:
“All proportional relationships are , but not all linear relationships are .
Directions: Fill in the blank with “Always”, “Sometimes” or “Never.” If “Sometimes,” justify your reasoning.
2. Equations of the form __________ show a proportional relationship.
3. In a translation, the slope __________ changes.
4. Equations of the form __________ show a proportional relationship.
5. A dilation __________ causes an image to have a different size.
Directions: For each of the equations given below, make a table of values and graph the line. Circle the slope in your equation and put a star next to the y-intercept in your equation. On the graphs, draw a right triangle to represent slope and put a star next to the y-intercept.
6. *
Slope (m): y-intercept (b): 0
x y
-4 1
0 0
4 -1
8 -2
7.
*
Slope (m):
y-intercept (b): -2
x y
-2 -3
0 -2
2 -1
4 0
linear proportional
sometimes
always never
SDUHSD Math B Honors Module #2 – TEACHER EDITION 2016-2017
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Directions: Solve each proportional equation. Show all of your work.8.
9.
10.
11.
12.
13.
Directions: Find the slope of the line represented in the graph, table of values or ordered pairs.
14. (3, -4) and (-2, 8)
15.
16. 17. (-5, 3) and (2, 7)
18. 19.
# of Raffle Tickets Total Cost
2 1
4 2
8 4
10 5
# of Lawns Total Earned
3 25.50
5 42.50
7 59.50
SDUHSD Math B Honors Module #2 – TEACHER EDITION 2016-2017
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20. Use dilations and proportionality to show that the equation of a line that goes through the origin and hasa slope of is . Explain your process.
21. Use dilations and proportionality to show that the equation of a line that goes through the point and has a slope of is
22. The equation of which of these lines can be derived by drawing one triangle with vertices (0,0), (1,0) and (1,2) and another similar triangle with vertices (0,0), (-2, 0) and (-2,-4)?
A. B.
C. D.
Explanation:
The rise for the right triangle formed from the point (3,1) and the origin is 1 and the run is 3. The point (x,y) on the line forms a right triangle where the rise is x and the run is y. Since the right triangles formed are dilations of one another, their corresponding parts are proportional; therefore . When solving for y, you get
Explanation:
The rise for the right triangle formed from the point (0,-2) with a slope of is 3 and the run is 2. Any point (x,y) on the line forms a right triangle where the rise is x and the run is y + 2. Since the right triangles formed are dilations of one another, their corresponding parts are
SDUHSD Math B Honors Module #2 – TEACHER EDITION 2016-2017
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23. Olivia used the proportion when deriving the equation of a line with similar trinagles. Whichstatement below is correct? Select two that apply.
A. The line has a slope of B. The line has a slope of
C. The line has a slope of D. The line has a y-intercept of
E. The line has a y-intercept of F. The line has a y-intercept of
24. Zach began deriving the equation of line by defining the lengths of line segments and as and , respectively. What proportion should he set up next using similar triangles and
A.
B.
C.
D.
25. BeBop Bakery and Moonlight Deli offer catering options for local businesses. The table below shows how much money each bakery charges for their catered meals.
a. Use the information in the table to graph BeBop Bakery and Moonlight Deli’s meal prices. Graph both lines on the same coordinate plane below. Label each line and label each axis.
b. What is the slope of the line representing BeBop Bakery? What does the slope represent in the context?
20; BeBop Bakery charges $20 per meal.
# of catered Meals
BeBop Bakery
Moonlight Deli
1 $20 $30
2 $40 $45
3 $60 $60
4 $80 $75
5 $100 $90
1 2 3 4 5
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 0
Number of Meals
SDUHSD Math B Honors Module #2 – TEACHER EDITION 2016-2017
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c. What is the slope of the line representing Moonlight Deli? What does the slope represent in thecontext?
15; Moonlight Deli charges $15 per meal.
d. What does the slope tell you about these two situations?
BeBop Bakery charges more than what Moonlight Deli charges per meal.
e. Explain the difference in y-intercepts.
The y-intercept for BeBop Bakery is 0. The y-intercept for Moonlight Deli is $15. Moonlight Deli charges an initial fee of $15, perhaps for delivery or set-up.
f. Write an equation for each situation.
BeBop Bakery: Moonlight Deli:
g. Which situation is a better deal? Explain your reasoning.
It depends on how many meals are ordered. If less than 3 meals are ordered, BeBop Bakery is less
expensive. If more than 3 meals are ordered, Moonlight Deli is less expensive. If exactly 3 meals are ordered, the cost would be the same for each place.
Spiral Review:
26. Solve for a. Assume all variables do not equal 0. Show all of your work.
27. Evaluate for and and . Show all of your work.
28. The length of a certain rectangle is 2 inches less than 3 times its width. If the perimeter of the rectangle is 44 inches, what is the area of the rectangle?
