p. 26 #11-15, 23-27, 37, 39, 45, 47
Dec 23, 2015
p. 26 #11-15, 23-27, 37, 39, 45, 47
p. 26 #11-15, 23-27, 37, 39, 45, 47
p. 26 #11-15, 23-27, 37, 39, 45, 47
1.4 Direct Variation and Proportion
Objectives: Write and apply direct variation equations. Write and solve proportions.
Standard: 2.8.11.P Analyze a relation to determine whether a direct or inverse variation exists and
represent it algebraically and graphically.
I. Determine whether each equation describes a direct variation.
y = 2x yesy = ½ x yes
y = 2x + 1 no
y = 3/x no
II. y varies directly as x. Find the constant of variation, k, and write an equation of direct variation that relates the two variables, y = kx.
Ex 1. y = -24 when x = 4 -24 = k (4)
k = -6 equation: y = -6x
Ex 2. y = -16 when x = 2 - 16 = k (2) k = -8 equation: y = -8x
Ex 3. y = 1 when x = ½ 1 = k (1/2) k = 2 equation: y = 2x
III. y varies directly as x.
Ex. 1. If y is 2.8 when x is 7, find y when x is - 4.
2.8 = k (7)
.4 = k
y = .4 (- 4)
y = -1.6
Ex. 2 If y is 6.3 when x is 70, find y when x is 5.4. 6.3 = k (70)
.09 = k
y = .09 (5.4)
y = .486
III. y varies directly as x.
• Ex. 3 If y is -5 when x is 2.5, find y when x is 6.
-5 = k (2.5)
-2 = k
y = -2 (6)
y = -12
IV. Use a direct variation equation to solve each word problem.
Ex 1. If 6 tickets cost $72, find the cost of 10 tickets.72 = k (6)12 = k
y = 12 (10) y = 120
Ex 2. If 3 CDs on sale cost $18, find the cost of 12 CDs.
18 = k (3)6 = k
y = 6 (12) y = 72
Ex 3. If 8 sodas cost $3.20, find the cost of 20 sodas.
y = 8
IV. Use a direct variation equation to solve each word problem.
Ex 4. Each day Jon rides his bicycle for exercise. When traveling a constant rate, he rides 4 miles in about 20 minutes. At this rate, how long would it take Jon to travel 7 miles? Recall that distance, d, rate, r, and elapsed time, t, are related by the equation d = rt.
V. Proportions
It is said that if y varies directly with x, then y isproportional to x. A proportion is a statement that two ratios are equal. A ratio is the comparison of 2 quantities by division.
. then ,If
:0 and 0For
bcaddc
ba
db
* Cross-Product Property of Property of Proportion
V. Proportions
means. theare and and extremes theare and
form theof proportion aIn
cbdad
c
b
a
The product of the means equals the product of the extremes: ad = bc
V. Proportions
Ex 1. w = 10 4 12
Ex 2. 3 = x
5 2
12w = 40
w = 40/12 w = 10/3
6 = 5xx = 6/5
V. Proportions
Ex 3. 3x –1 = x 5 2
2 (3x – 1) = 5x
6x - 2 = 5x
x = 2
Application - Physics
Lesson Quiz
Homework
Packet sheet 1.4
OR
p. 33 #14-19 and p. 34 # 32-34, #45-48
Quiz on 1.1 – 1.5 this Wednesday