1. Real World Applications
Blue day – 3/9/15
Gold day – 3/10/15
Real World Applications

2. Slope-Intercept Form
Word problems with linear equations will be in slope-intercept form if you are given the following information:
the slope (m) - the rate of change
the y-intercept (b) - the starting (initial) value

3. Example 1
A closet organizer charges a $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is graphed below.
a. Write an equation that represents the cost as a function of the number of hours.
for each hour
Cost
$30
plus is
$100 •x + y = 30
100
An equation is y = 30x

4. Example 1 - Continued
A closet organizer charges $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is graphed below.
b. Identify the slope and y-intercept and describe their meanings.
The y-intercept is 100. This is the cost for 0 hours, or the initial fee of $100. The slope is 30. This is the rate of change of the cost: $30 per hour.
c. Find the cost if the organizer works 12 hrs.
y = 30x + 100
Substitute 12 for x in the equation
= 30(12) = 460
The cost of the organizer for 12 hours is $460.

5. Example 2
A caterer charges a $200 fee plus $18 per person served. The cost as a function of the number of guests is shown in the graph.
a. Write an equation that represents the cost as a function of the number of guests.
for each meal
Cost is
$18
plus
$200 y = +
200 18 •x
An equation is y = 18x

6. Example 2 Continued…
A caterer charges a $200 fee plus $18 per person served. The cost as a function of the number of guests is shown in the graph.
b. Identify the slope and y-intercept and describe their meanings.
The y-intercept is 200. This is the cost for 0 people, or the initial fee of $200. The slope is 18. This is the rate of change of the cost: $18 per person.
c. Find the cost of catering an event for 200 guests.
y = 18x + 200
Substitute 200 for x in the equation
= 18(200) = 3800
The cost of catering for 200 people is $3800.

7. WS 1
Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, L, after d days. In how many days will the water level be 26 feet?

8. WS 2
For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, C, after h hours of babysitting. What do you think the slope and the y-intercept represent? How much money will she make if she baby-sits 5 hours?

9. WS 3
A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work?