Transcript PowerPoint

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 water
and is leaking at a rate of 15 gal/min. Write
a linear equation representing the tank volume
in terms of time.
Let x = # minutes
Let y = volume in gallons
y  600  15x
Two Points
The volume in a water tank after 10 minutes
is 450 gallons. After 30 minutes, the volume
in the tank is 150 gallons. Write an equation
representing the volume in terms of time.
Let x = # minutes
Let y = volume in gallons
 x1, y1   10,450
 x 2 , y2    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
Write a linear equation to describe each situation.
Point and Slope
A sky diver jumps from a
plane at 11,000 ft. above the
ground and descends at
15 ft./sec.
y = height (ft.)
x = time (sec.)
Start Value = b = 11,000
Change = m = -15
Two Points
A sky diver jumps from a
plane. He is 10,100 ft. above
the ground after 60 sec. and
is 8300 ft. after 3 min.
(x1 , y1 )  (60, 10,100)
(x 2 , y 2 )  (180, 8300)
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.
Slope
Change in price = $0.80/ brick
m = 0.80
Point
500 bricks cost $465
(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
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)
y2- y 1
m=
= 18.05 - 6.20
x2- x 1
20 - 5
m = 11.85 = 0.79
15
y = 0.79x + 2.25
y = mx + b
y = 0.79x + b
6.20 = 0.79(5) + b
6.20 = 3.95 + b
-3.95 -3.95
2.25 = b
r = -3p +12
m = -3
b = 12
# Rulers
Pens cost $3 each and rulers cost $1 each. If Jim
spends $12, how many of each did he buy?
Let p = # of pens purchased
Let r = # of rulers purchased
12
3p + 1r = 12
-3p
-3p
10
1r = -3p +12
8
6
4
2
0
1
2
3
# Pens
4
5