A lesson on interpreting slope and y-intercept in real
world examples
Standard:
MAFS.912.S-ID.3.7:
Interpret the slope (rate of change) and the intercept (constant
term) of a linear model in the context of the data.
Problem of the Day:
Solve for the slope between (-1,-5) and (6,9).
m= y2-y1
x2-x1
m= 9-(-1)
6-(-1)
m= 14
7
m=2
Slope intercept form- y=mx+b, where m is slope and b is the yintercept
Slope- Change in y over change in x (rate of change)
Y-intercept- the value of y when x is zero
Example of Slope in a Real World Scenario
The graph to the right
shows the growth of a
tree at a constant rate,
over a period of four
years. Interpret the slope
of the line.
m= Change in height
Change in time
Example of
Slope in a
Real World
Scenario
m= change in distance
change in time
.
Example of Y-Intercept in a Real World Scenario
For example: The yintercept in this
graph is 1080,
meaning it is the
amount the person
owes before he/she
began making
payments. (zero
payments have been
made, $1080 owed)
The graph then shows that over the next 24 months this
debt will be paid off.
Example of Y-Intercept in a Real World Scenario
You have 300 items of clothing
and decide to start donating to
Goodwill. Your y-intercept is the
amount of clothing you have
before you start donating to
Goodwill every month.
Solving a Real World Example
 A student is eating an ice
cream cone at the park that is
12.7cm tall. It is extremely hot
outside and the ice cream
starts to melt at a constant
rate of 2cm/minute. If the
student didn’t eat any of the
ice cream and it started to
melt, how much would be left
after 3 minutes?
 1st: Identify the slope and y-
intercept
 2nd: Plug into slope intercept
form
 Y=-2x+12.7 (slope is negative
because it is decreasing in
size)
 3rd: Plug in 3 for x since we




want to know how tall it will
be after 3 minutes
4th: Solve
y=-2(3)+12.7
y=-6+12.7
y=6.7
Understand that after 3 minutes of melting the ice cream cone will now measure
6.7cm.
Leaky Lines Project
 Items you should have:
 400ml of water
 500ml+ graduated
cylinder
 Empty water bottle
 Stopwatch
Leaky Lines Project
 Get into groups of two
 One person will hold
the water bottle and be
in charge of the
stopwatch
 Measure 400ml into
bottle
 Turn water bottle over
and start timer
 Every 10 seconds record
how much water has
accumulated in the
cylinder
Leaky Lines Project
 Create a graph based on
the data gathered
graphing the time
intervals on the x-axis
and the amount of
milliliters on the y-axis.
 Solve for the rate of
change between two
coordinates.
 Write the equation of
the line.
 Discussion:
 Is the slope positive or
negative?
 What is the y-intercept?
Independent Practice
 Had we been
measuring the rate at
which the water left the
bottle, would the slope
have been positive or
negative?
 What would the yintercept have been?
 Write an equation
expressing this linear
relationship using m
for slope.
Review for Quiz
Your family is taking a trip to Disney and is driving at
a constant rate. After one hour, you have traveled 60
miles, and after 2 hours you have traveled 120 miles.
How fast is the car going?
2. You are selling candy bars for a fundraiser. You have
raised $50 so far and sell each candy bar for 75 cents.
How much money will you have made after selling 30
candy bars?
1.
Review for Quiz Continued
 The graph shows the
amount of money you have
at the beginning of the
month.
a. How much money
did you begin with?
b. How much money
do you earn each
week?
c. How much money
will you have after 3
weeks?