Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solving Problems: A Chemistry Handbook
Chemistry: Matter and Change
19
SOLVING PROBLEMS:
A CHEMISTRY HANDBOOK
CHAPTER
2
If a best fit line is straight, there is a linear relationship between
the variables. This relationship can be described by the steepness, or
slope, of the line. If the line rises to the right, the slope is positive. A
positive slope indicates that the dependent variable increases as the
independent variable increases. If the line falls to the right, the slope
is negative. A negative slope indicates that the dependent variable
decreases as the independent variable increases. You can use two
data points to calculate the slope of a line.
Example Problem 2-11
Calculating the Slope of a Line from Data Points
Calculate the slope of a line that contains these data points:
(3.0 cm 3 , 6.0 g) and (12 cm 3 , 24 g).
To calculate the slope of a line from data points, substitute the
values into the following equation.
slope ϭ
ϭ⌬ y/⌬x
slope ϭ
ϭ
ϭ 2.0 g/cm 3
Practice Problems
26. Calculate the slope of each line using the points given.
a. (24 cm 3 , 36 g), (12 cm 3 , 18 g)
b. (25.6 cm 3 , 28.16 g), (17.3 cm 3 , 19.03 g)
c. (15s, 147 m), (21 s, 205.8 m)
d. (55 kJ, 18.75°C), (75 kJ, 75.00°C)
Interpreting data When you are asked to read the information
from a graph, first identify the dependent variable and the independent variable. Look at the ranges of the data and think about what
measurements were taken to obtain the data. Determine whether the
relationship between the variables is linear or nonlinear. If the relationship is linear, determine if the slope is positive or negative.
▲
18 g
ᎏ
9.0 cm 3
24 g Ϫ 6.0 g
ᎏᎏ
12 cm 3 Ϫ 3.0 cm 3
y 2 Ϫ y 1
ᎏ
x 2 Ϫ x 1
Solving Problems: A Chemistry Handbook
Chemistry: Matter and Change
19
SOLVING PROBLEMS:
A CHEMISTRY HANDBOOK
CHAPTER
2
If a best fit line is straight, there is a linear relationship between
the variables. This relationship can be described by the steepness, or
slope, of the line. If the line rises to the right, the slope is positive. A
positive slope indicates that the dependent variable increases as the
independent variable increases. If the line falls to the right, the slope
is negative. A negative slope indicates that the dependent variable
decreases as the independent variable increases. You can use two
data points to calculate the slope of a line.
Example Problem 2-11
Calculating the Slope of a Line from Data Points
Calculate the slope of a line that contains these data points:
(3.0 cm 3 , 6.0 g) and (12 cm 3 , 24 g).
To calculate the slope of a line from data points, substitute the
values into the following equation.
slope ϭ
ϭ⌬ y/⌬x
slope ϭ
ϭ
ϭ 2.0 g/cm 3
Practice Problems
26. Calculate the slope of each line using the points given.
a. (24 cm 3 , 36 g), (12 cm 3 , 18 g)
b. (25.6 cm 3 , 28.16 g), (17.3 cm 3 , 19.03 g)
c. (15s, 147 m), (21 s, 205.8 m)
d. (55 kJ, 18.75°C), (75 kJ, 75.00°C)
Interpreting data When you are asked to read the information
from a graph, first identify the dependent variable and the independent variable. Look at the ranges of the data and think about what
measurements were taken to obtain the data. Determine whether the
relationship between the variables is linear or nonlinear. If the relationship is linear, determine if the slope is positive or negative.
▲
18 g
ᎏ
9.0 cm 3
24 g Ϫ 6.0 g
ᎏᎏ
12 cm 3 Ϫ 3.0 cm 3
y 2 Ϫ y 1
ᎏ
x 2 Ϫ x 1