The document presents a lesson about solving word problems with linear models, focusing on interpreting linear graphs, identifying intercepts, and calculating slopes. It explains concepts such as the line of best fit and provides an example of determining temperature changes over time, ultimately leading to the formulation of the equation of the line in slope-intercept form. Students are tasked with predicting the temperature of a liquid after a specified time using the derived equation.

1. Solving word problems involving linear graphs
PROBLEM
SOLVING WITH
LINEAR MODELS
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0
0
0
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2. 0
LESSON
OUTLINE
Linear Models and Equations
Interpreting Linear Models
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3. CAN ALL DATA SETS BE
SHOWN ON A GRAPH IN
AN “ORDERLY”
MANNER?
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4. 0
LEARNING
OUTCOMES
Identify and interpret the
intercept of a linear model.
Intercept:
the point where the line
intersects the y-axis
Slope:
the ratio of change in y to
change in x between two
points in a line
Calculate and interpret the
slope of a linear model.
State the equation of the line
in slope-intercept form.
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5. NOT ALL DATA SETS
CAN LEAD TO AN
“ORDERED” SET.
A set of data may be
scattered as the one
shown in the graph but
can be represented by a
line of best fit.
LINE OF BEST FIT:
A straight line that best represents a
set of scattered data.
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6. 0
0
0
0
LINE OF
BEST FIT
2
0
10
20
4 6 8 10 12 14 16
30
40
50
TIME
(min)
TEMPERATURE
(°C)
After gathering the data,
your group drew the line
of best fit as shown.
Can you identify the
intercept?
In an experiment for your Science class, you
investigated how fast a given liquid changes
its temperature.
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7. IDENTIFYING THE
INTERCEPT OF
THE LINE
Recall that the y-intercept refers to
the point where the line intersects the
y-ax
is.
Looking at the graph, the line
intersects the y-axis at 25.
The y-intercept is thus 25.
2
0
10
20
4 6 8 10 12 14 16
30
40
50
TIME
(min)
TEMPERATURE
(°C)
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8. INTERPRETING
THE INTERCEPT
OF THE LINE
What information can the y-intercept
tell us?
The y-intercept is also the value of y
when x = 0.
Looking at the graph again, we can
then say that the temperature of the
liquid before heating (time = 0), is
25°C.
2
0
10
20
4 6 8 10 12 14 16
30
40
50
TIME
(min)
TEMPERATURE
(°C)
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9. y - y
x - x
2
2
1
1
change in y
change in x
CALCULATING THE
SLOPE OF THE LINE
Slope is the ratio of the change in y
and the change in x.
This can be calculated using two
poi
nts on the line with the formula:
slope (m) =
slope (m) =
TRY TO SOLVE
FOR THE
SLOPE OF THE
LINE!
2
0
10
20
4 6 8 10 12 14 16
30
40
50
TIME
(min)
TEMPERATURE
(degrees
Celsius)
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10. 40 - 35
7 - 5
CALCULATING THE
SLOPE OF THE LINE
Using the marked two points on the line:
This slope tells us that the temperature
increases by 2.5°C every minute
slope (m) =
slope (m) =
m = 2.5
2
0
10
20
4 6 8 10 12 14 16
30
40
50
TIME
(min)
TEMPERATURE
(degrees
Celsius)
ANSWER KEY
y - y
x - x
2
2
1
1
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11. 0
0
0
EQUATION OF
THE LINE IN
SLOPE-INTERCEPT
FORM
Using the y-intercept (b) and the
slope (m), the line of best fit may be
represented through an equation.
Equation of a line in
slope intercept form:
y = mx+ b
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12. 2
0
10
20
4 6 8 10 12 14 16
30
40
50
TIME
(min)
TEMPERATURE
(degrees
Celsius)
STATING THE
EQUATION OF
THE LINE
Given these:
The equation of the line is:
This equation can now be used to
predict the temperature at a given time.
m = 2.5
y = 2.5x+ 25
b = 25
y = mx+ b
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13. ANSWER KEY
ACTIVITY: USING
THE EQUATION
OF THE LINE
Predict the temperature of the liquid
after 15 minutes of heating.
y = 2.5x+ 25
y = 2.5x+ 25
y = 2.5 (15) + 25
y = 62.5°C
After 15 minutes of heating, the temperature
of the liquid is predicted to be 62.5°C.
Asked:
Temperature (y)
at 15 minutes (x)
Solution:
using the equation
of the line
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