Objective - To solve word problems involving linear situations.

Three types of word problems

1) Point/Slope

2) Two Points

3) Two Things and a Total

Point - Slope Problem

A water tank contains 600 gallons of waterand is leaking at a rate of 15 gal/min. Writea linear equation representing the tank volume in terms of time.

Let x = # minutesLet y = volume in gallons

y 600 15x

Two Points

The volume in a water tank after 10 minutesis 450 gallons. After 30 minutes, the volume in the tank is 150 gallons. Write an equation representing the volume in terms of time.

1 1x , y

Let x = # minutesLet y = volume in gallons

2 2x , y

10,450

30,150

Two Things and a Total

Sandwiches cost $3 each and sodas cost $2 each. If Sam spent a total of $24, how many of each could he have bought?

Let x = # of sandwiches

Let y = # of sodas

3x 2y 24

Start Value =

Point and Slope Two Points

A sky diver jumps from aplane at 11,000 ft. above the ground and descends at 15 ft./sec.

A sky diver jumps from aplane. He is 10,100 ft. abovethe ground after 60 sec. andis 8300 ft. after 3 min.

b = 11,000

Change = m = -15

1 1(x , y ) (60, 10,100)

2 2(x , y ) (180, 8300)

y = height (ft.)

x = time (sec.)

Write a linear equation to describe each situation.

A masonry company charges $0.80 a brick. The company will charge $465 for 500 bricks to be delivered to a site. If x = the number of bricks, and y = total cost, write an equation for y in terms of x.

Change in price = $0.80/ brick

500 bricks cost $465

m = 0.80

(x, y) = (500, 465)

y = mx + b

y = 0.80x + b

465 = 0.8(500) + b

465 = 400 + b-400 -400

65 = b

y = 0.8x + 65

Slope

Point

11.85

18.05 - 6.20

Suppose a 5 minute call costs $6.20 and a 20 minute call costs $18.05. Write an equation which describes cost y in terms of x minutes.

(minutes, cost)(x, y)

(5, 6.20) (20, 18.05)

m =y2- y1

x2- x1

=20 - 5

m = 15

= 0.79

y = mx + b

y = 0.79x + b

6.20 = 0.79(5) + b

6.20 = 3.95 + b-3.95 -3.95

2.25 = by = 0.79x + 2.25

0 1 2 3 4 5

Pens cost $3 each and rulers cost $1 each. If Jim spends $12, how many of each did he buy?

Let r = # of rulers purchasedLet p = # of pens purchased

3p + 1r = 12-3p -3p

1r = -3p +12

r = -3p +12

m = -3

b = 12

# R

uler

s

# Pens

12

10

8

6

4

2