How do you know what 1400 and -350 mean in the context of the scenario?

A pool is being emptied. The equation to model the remaining water (W) at time (t)

is W = 1400 – 350t

In this lesson you will learn how to interpret the rate of

change and the y-intercept in context by examining each of

the four representations.

Let’s ReviewLet’s Review

Rate of change (slope)

x (days late)

y (late fees)

1 $0.50

2 $1.00

3 $1.50

4 $2.00

= 0.50

1.00 – 0.502 - 1 0.501

Initial value (y-intercept)

= 0

Let’s ReviewA Common Mistake

Suppose a car is traveling 35 miles per hour. An equation could be D = 35h, where

D is distance after h hours.

What does 35 mean within the context of the scenario?The car goes 35 miles.

Incorrect !

The car travels 35 miles for every hour that passes.

Let’s ReviewCore Lesson

A 1400 gallon pool is being emptied at a rate of 350 gallons per hour.

W = -350T + 1400

T (hours)

W (remaining

gallons)

0 1400

1 1050

2 700

3 350

100

Let’s ReviewCore Lesson

Rate of change (slope) =

Initial value (y-intercept) =-350 1400

Meaning: The pool is losing 350 gallons of water every hour.Meaning: The pool has 1400 gallons before it begins to drain.

In this lesson you have learned how to interpret the rate of

change and the y-intercept in context by examining each of

the four representations.

Let’s ReviewGuided Practice

A car rental agency charges $30 plus $0.25 per mile for each mile driven.

C = 30 + 0.25m

Identify the slope and y-intercept in each representation. Explain the meaning of each.

m (miles)

C (cost)

0 $30

4 $31

8 $32

12 $33

Let’s ReviewExtension Activities

Show an image of a restaurant price board or menu. -Are the prices slopes or y-intercepts?-What does each mean as it pertains to the restaurant?-There is an unseen value for each of the prices, what is it (slope or y-intercept)?-What does the unseen value mean as it pertains to the restaurant?

Let’s ReviewExtension Activities

Think of a situation pertaining to your life that would have a slope and y-intercept.

Share the situation, slope, y-intercept, and meaning within the situation.

Let’s ReviewQuick Quiz

A restaurant charges $150 for a room and $10 per person for food and drinks. What is the slope and what does it mean in the context of the scenario?

a) Total increases $10 for the room cost.b) Total increases $10 for every added personc) Total is $150 for the room cost.d) Total is $150 for every added person.

Let’s ReviewQuick Quiz

A restaurant charges $150 for a room and $10 per person for food and drinks. What is the y-intercept and what does it mean in the context of the scenario?

a) Total is $10 with zero people attending.b) Total increases $10 for every added personc) Total is $150 with zero people attending.d) Total is $150 for every added person.