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