Constructing Linear Function Models of Data (3.11.1)

Question 1

• Slope can be very useful for the examination of data.

Answer 1

• Slope can be very useful for the examination of data.

Question 2

• Frequently a straight-line approximation of the graph of the data shows the pattern of change involved in the real-world situation.

Answer 2

• Frequently a straight-line approximation of the graph of the data shows the pattern of change involved in the real-world situation.

Question 3

• It is often possible to write an equation that fits the data, to not only see trends to date but make predictions into the future.

Answer 3

• It is often possible to write an equation that fits the data, to not only see trends to date but make predictions into the future.

Question 4

This application shows data related to AIDS.
The graph is set up in the typical way with the time changing
along the x-axis and the reported data plotted along the y-axis.
The number of cases reported in 1986 is the first point of
data. The number of cases reported in 1994 is the last point
graphed.
The actual data produces a line graph with a slight curve.
You may work with the problem by adding a straight line
that approximates the curve. Here we mark the line at the
starting and ending points of the data curve.
With a straight line, we can measure constant change from
one point in time to another. We can also develop an equation
to represent the general pattern of change in the data.
Remember: slope measures change with vertical change
placed over horizontal change. To calculate slope here, the
first and last points were used. The slope is the difference
between the number of cases reported over the number of
years in the study.
Remember: The slope-intercept form for the equation for
a line is: y = mx + b.
Substitute your slope of 6,325 for m.
Substitute 11,900 in for the y-intercept, b.
You have your equation.
You want to predict the number of cases likely to be reported
in the year 2000. That will be 14 years since the first year of
reporting.
Let x = 14 and solve.

Answer 4

This application shows data related to AIDS.
The graph is set up in the typical way with the time changing
along the x-axis and the reported data plotted along the y-axis.
The number of cases reported in 1986 is the first point of
data. The number of cases reported in 1994 is the last point
graphed.
The actual data produces a line graph with a slight curve.
You may work with the problem by adding a straight line
that approximates the curve. Here we mark the line at the
starting and ending points of the data curve.
With a straight line, we can measure constant change from
one point in time to another. We can also develop an equation
to represent the general pattern of change in the data.
Remember: slope measures change with vertical change
placed over horizontal change. To calculate slope here, the
first and last points were used. The slope is the difference
between the number of cases reported over the number of
years in the study.
Remember: The slope-intercept form for the equation for
a line is: y = mx + b.
Substitute your slope of 6,325 for m.
Substitute 11,900 in for the y-intercept, b.
You have your equation.
You want to predict the number of cases likely to be reported
in the year 2000. That will be 14 years since the first year of
reporting.
Let x = 14 and solve.