Download Algebra 2 Using Linear Models

Bellwork 9/15/2014
Algebra 2
Atlanta, GA has an elevation of 15 ft above
sea level. A hot air balloon taking off from
Atlanta rises 40 ft/min. Write an equation to
model the balloon's elevation as a function
of time. Interpret the intercept of which the
graph intersects the vertical axes.
Using Linear Models
Lesson 2-4
Additional Examples
Algebra 2
Suppose an airplane descends at a rate of 300 ft/min from
an elevation of 8000 ft.
Write and graph an equation to model the plane’s elevation as a function
of the time it has been descending. Interpret the intercept at which the
graph intersects the vertical axis.
Relate: plane’s elevation = rate • time + starting elevation .
Define: Let t = time (in minutes) since the plane began its descent.
Let d = the plane’s elevation.
Write: d = –300 • t + 8000
Using Linear Models
Lesson 2-4
Additional Examples
Algebra 2
(continued)
An equation that models the plane’s elevation is d = –300t + 8000.
The d-intercept is (0, 8000).
This tells you that the elevation of the plane was 8000 ft at the moment
it began its descent.
Using Linear Models
Lesson 2-4
Additional Examples
Algebra 2
A spring has a length of 8 cm when a 20-g mass is hanging
at the bottom end. Each additional gram stretches the spring
another 0.15 cm. Write an equation for the length y of the spring as
a function of the mass x of the attached weight. Graph the equation.
Interpret the y-intercept.
Step 1: Identify the slope.
0.15 or 3/20
Using Linear Models
Lesson 2-4
Algebra 2
Additional Examples
(continued)
Step 2: Use one of the points and the slope-intercept form to
write an equation for the line.
y = mx + b
8 = 3/20(20) + b
8=3+b
5=b
y = 0.15x + 5
Use the slope-intercept form.
Substitute.
Solve for y.
Using Linear Models
Lesson 2-4
Additional Examples
Algebra 2
(continued)
An equation of the line that models the length of the spring is y = 0.15x + 5.
The y-intercept is (0, 5). So, when no weight is attached to the spring, the
length of the spring is 5 cm.
Using Linear Models
Lesson 2-4
Algebra 2
Additional Examples
Use the equation from Additional Example 2. What mass
would be needed to stretch the spring to a length of 9.5 cm?
y = 0.15x + 5
9.5 = 0.15x + 5
9.5 – 5
=x
0.15
30 = x
The mass should be 30 g.
Write the equation.
Substitute 9.5 for y.
Solve for x.
Simplify.
Using Linear Models
Algebra 2
Scatter Plot: graph that relates two different sets of data by plotting
the data as ordered pairs.
Using Linear Models
Algebra 2
A
D
B
E
C
No Correlation
Weak Positive Correlation
Weak Negative Correlation
Strong Positive Correlation
Strong Negative
Correlation
Using Linear Models
Lesson 2-4
Algebra 2
Additional Examples
An art expert visited a gallery and jotted down her guesses
for the selling price of five different paintings. Then, she checked the
actual prices. The data points (guess, actual) show the results, where
each number is in thousands of dollars. Graph the data points.
Decide whether a linear model is reasonable. If so, draw a trend line
and write its equation.
{(12, 11), (7, 8.5), (10, 12), (5, 3.8), (9, 10)}
A linear model seems reasonable since the points
fall close to a line.
Trend lines and equations may vary.
Using Linear Models
Lesson 2-4
Additional Examples
Algebra 2
(continued)
A linear model seems reasonable since the points fall close to a line. A
possible trend line is the line through (6, 6) and (10.5, 11). Using these
two points to write an equation in slope-intercept form gives
10
2
y= 9 x– 3.
Using Linear Models
Algebra 2