Math Sections 7.5 and 7.6

Definitions

100

What variable represents the constant of variation?

k

200

What is the y-intercept for a proportional equation?

(0, 0)

300

What is the general form for proportional equations?

y=kx

400

What variable represents the output of a direct variation equation?

y

500

What is direct variation?

Direct variation is the relationship between two quantities where one is a constant multiple of the other.

Constants of Variation

100

What is the constant of variation for this table?

x   l   2   l   3   l   4   l

y   l   4   l   6   l   8   l

k=2

200

What is the constant of variation for this table?

x   l   2   l   3   l   4   l

y   l   6   l   9   l   12   l

k = 3

300

What is the constant of variation for this table?

x   l   2   l   4   l   6   l

y   l   1   l   2   l   3   l

k = 1/2

400

What is the constant of variation for this table?

x   l   6    l   8    l   10   l

y   l   -3   l   -4   l   -5   l

k = -1/2

500

What is the constant of variation for this table?

x   l   14   l   21   l   28   l

y   l   -2   l   -3   l   -4   l

k = -1/7

Direct Variation Equations

100

Write the equation for this table.

x   l   1   l   2   l   3   l

y   l   2   l   4   l   6   l

y = 2x

200

Write the equation for this table.

x   l   3   l   6   l   9   l

y   l   1   l   2   l   3   l

y = 1/3x

300

Write the equation for this table.

x   l   1    l   2      l   3   l

y   l   -5   l   -10   l   -15   l

y = -5x

400

Write the equation for the cost of tomatoes from Yana's tomato stand.

t   l   2          l   4         l   8         l

c   l   $1.50   l   $3.00   l   $6.00   l

c = 0.75t

500

Write the equation for the cost of popcorn from David's popcorn stand.

p   l   3          l   5          l   8           l

c   l   $9.48   l   $15.80   l   $25.28   l

c = 3.16p

Table of Values Problems

100

Write the equation for the cost of peanuts from Dima's peanut stand. Then find the cost for 15 bags of peanuts.

p   l   2          l   4         l   8           l

c   l   $4        l   $8       l   $16.00   l

c = 2p

$30

200

Write the equation for the cost of hotdogs from Vlad's hotdog stand. Then find the cost for 120 hotdogs.

h   l   3          l   6          l   10         l

c   l   $4.50    l   $9.00   l   $15.00   l

c = 1.50h

$180

300

Write the equation for the cost of bagels from Irina's bagel stand. Then find the cost for 57 bagels.

b   l   4          l   2          l   7         l

c   l   $4.60    l   $2.30   l   $8.05   l

c = 1.15b

$65.55

400

Write the equation for the cost of burgers from Anton's burger stand. Then find the cost for 108 burgers.

b   l   2          l   3          l   5         l

c   l   $5.28    l   $7.92   l   $13.20   l

c = 2.64b

$285.12

500

Write the equation for the cost of french fries from Venessa's french fries stand. Then find the cost for 1,245 bags of french fries.

f   l   1          l   3          l   12         l

c   l   $1.17    l   $3.51   l   $14.04   l

c = 1.17f

$1,456.65

Parabolas

100

Complete the table of values for the equation.

y = x² - 2x + 1

x  l  y

0  l

1  l

x  l  y

0  l  1

1  l  0

200

Complete the table of values for the equation.

y = x² - 3x + 4

x  l  y

0  l

1  l

2  l

x  l  y

0  l  4

1  l  2

2  l  2

300

Complete the table of values for the equation.

y = x² - 5x + 7

x  l  y

0  l

1  l

2  l

3  l

x  l  y

0  l  7  

1  l  3

2  l  1

3  l  1

400

Complete the table of values for the equation.

y = x² - 7x + 9

x  l  y

0  l

1  l

2  l

3  l

4  l

x  l  y

0  l  9

1  l  3

2  l -1

3  l -3

4  l -3

500

Complete the table of values for the equation.

y = x² - 10x + 15

x  l  y

0  l

1  l

2  l

3  l

4  l

5  l

x  l  y

0  l 15

1  l  6

2  l -1

3  l -6

4  l -9

5  l -10