Direct Proportion
Representing Direct or Inverse Proportion Graphically
Real-world Situation: Direct proportional
Inverse Proportion
Real-world Situation: Increase/Decrease
100
What is the equation for Direct Proportion?
y = kx
100
State whether the graph represents a direct proportion. _______________
2. What is the Constant Proportionality?
3. What is the Direct Proportion equation?
1.Yes
2.C.P. = 100
3. y=100x
100
Julia pays $40 for 8 T-shirts at a store. Given that the cost of T-shirts is directly proportional to the number of T-shirts she buys, use proportionality reasoning to find the cost of 5 T-shirts.
100
What is the equation for Inverse Proportion
y = k/x
100
The cost price of a box of cereal is $1.80. The markup for each box of cereal is 60%. Find the selling price of each box of cereal.
100% + 60% = 160% ---at 60% mark up
160% of $1.80 = 160/100 ∙ $1.80
= $2.88
The selling price of each box of cereal is $2.88.
200
What is the Constant Proportionality equation for Direct Proportion?
k = y/x
200
1. State whether the graph represents a direct proportion. _______________
2. If yes, What is the Constant Proportionality?
3. If yes, what is the Direct Proportion Equation?
No
200
m varies directly as n, and m = 14 when n = 7
a. Write an equation that relates m and n.
b Find m when n = 16.
c Find n when m = 30.
a. m =2n
b. m = 32
c. n = 15
200
What is the equation for the Constant Proportionality of an Inverse Proportion
k = xy
200
At a store, the price of a box of chocolates is $12.50. During a sale, the price of the chocolates is $11. Find the percent of discount during the sale.
$12.50 – $11 = $1.50 ----Mark down
1.5/12.5 ∙ 100% = 12%
The percent of discount is 12% during the sale.
300
Determine if 3y - 1/2x is a Direct Proportion equation. If yes, what is the Constant Proportionality?
Yes, 1/6
300
1. State whether the graph represents an Inverse Proportion
2. If yes, find the constant of proportionality from the graph.
1. Yes
2. 12
300
p varies directly as q, and p = 6 when q = 30
a Write an equation that relates p and q.
b Find q when p = 10.
c Find p when q = 7.
a. p = 1/5q
b. 50
c. 7/5
300
1. Determine if the equation is Inversely Proportion,
1/2y = 5/x.
2. What is the Inversely Proportion equation?
3. What is the Constant Proportionality?
1. Yes
2. y = 10/x
3. k = 10
300
The original cost of a bicycle is $450. The selling price of the bicycle at a retail store is $585. Find the percent markup.
$585 − $450 = $135 -----the difference between the two price
$135/$450 x 100% ----markup value divided by original price x 100%
400
2y -5 = x
No
400
1. State whether the graph is inverse proportion
2. If yes, find the consent Proportionality
1. Yes
2. 24
400
The number of eggs used, E (12) , is directly proportional to the number of cakes baked, C (3).
What is the Constant Proportionality?
12/3
400
What is the inverse Proportion equation for the graph?
What is the Constant Proportionality?
y = k/x = (60)/ 6 = 10
k = xy = 60, k= 60
400
The original price of a remote control car was $80. During a sale, its price became $64. Find the percent discount.
$80 - $64 = $16
$16/$80 x 100% = 20%
500
Determine whether y is Directly Proportional to x. _____________________
If yes, the Constant Proportionality ________________________
Yes, 1.6
500
1. Find the Constant Proportionality of the graph
2. What is the Inverse Proportion equation?
1. 24
2. x*y = 24
500
The number of pears for sale at an orchard, P (200), is directly proportional to the number of crates used to pack the pears, C(10). The table shows the relationship between the total number of pears for sale and the number of crates.
Write a direct proportion equation that relates P and C
P = 20C
500
Constant of proportionality: tr = 2 ∙ 300 = 600
Inverse proportion equation: rt = 600
500
Alex deposited $1,200 into a savings account. At the end of the first year, the amount of money in the account increased to $1,260. What was the percent interest?
$1260 - $1200 = $60
$60/$1200 x 100 -----difference/original x 100%
5%