This document provides examples of how to interpret slope and y-intercept in real-world contexts. It defines slope as the rate of change and y-intercept as the value of y when x is zero. Examples given include using slope to show the growth rate of a tree over time, and using the y-intercept to represent an initial debt amount before payments are made. It also works through an example of using slope-intercept form to model the melting of an ice cream cone over time and calculate how tall it would be after 3 minutes.

1. A lesson on interpreting slope and y-intercept in real
world examples

2. 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.

3. Problem of the Day:
Solve for the slope between (-1,-5) and (6,9).
m=2
m= y2-y1
x2-x1
m= 9-(-1)
6-(-1)
m= 14
7

4. Slope intercept form- y=mx+b, where m is slope and b is the y-
intercept
Slope- Change in y over change in x (rate of change)
Y-intercept- the value of y when x is zero

5. Example of Slope in a Real World Scenario
m= Change in height
Change in time
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.

6. Example of
Slope in a
Real World
Scenario
m= change in distance
change in time

7. Example of Y-Intercept in a Real World Scenario
.
For example: The y-
intercept 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.

8. 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.

9. 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.