## Transcribed Text

Linear Functions Problem
Inputs (x ) x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Population Problem
Outputs (y )
This problem has you compare various linear functions.
y =-5x +3
y =-2x +3
y = 0x + 3
y = 2x + 3
y = 5x + 3
a.) Enter formulas for the 5 different linear functions which can be filled down that will output the appropriate 𝑦𝑦-value for the given 𝑥𝑥-values.
b.)
What is the 𝑦𝑦-intercept of each function? Answer should be a number. Make a single scatterplot (connect the dots) showing all 5 lines.
c.) Which slope from the 5 different linear functions will give the largest 𝑦𝑦-value for 𝑥𝑥 = -1.5? Answer should be a number.
d.) Will a positive or negative slope cause the graph to move downward from left to right? Answer should be the word positive or negative.
Part b: Part c: Part d:
e.)
This problem has you compare various linear functions.
a.) Create a scatterplot of the data and insert trendline and display equation.
U.S. Census Year 1790
1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Years Since 1950
U.S. Population
3,929,214
5,308,483 7,239,881 9,638,453
12,866,020 17,069,453 23,191,876 31,443,321 38,558,371 50,189,209 62,979,766 76,212,168 92,228,496
106,021,537 123,202,624 132,164,569 151,325,798 179,323,175 203,211,926 226,545,805 248,709,873 281,421,906 308,745,538
U.S. Population 151,325,798
179,323,175 203,211,926 226,545,805 248,709,873 281,421,906 308,745,538
Slope:
Intercept:
From Equation:
Using SLOPE and INTERCEPT:
From Equation:
Using SLOPE and INTERCEPT:
.
b.) Note in the equation on the scatterplot that the slope and 𝑦𝑦-intercept have been entered in scientific notation. Type in the slope and 𝑦𝑦-intercept without using scientific notation. Format with commas and no decimal places.
c.) Now use the built-in SLOPE and INTERCEPT functions to find exact values. Format to zero decimal places.
d.) Enter a formula that uses the values from part c to predict the U.S. population in 2050. Format with commas and no decimal places.
2050 Estimate: Part d:
Slope:
2050 Estimate: Part i:
The
is changing by
e.) Interpret the SLOPE value in a sentence by filling in the blanks in the sentence below.
The ___i____ is changing by ____ii_____ ___iii____ per __iv___.
i
ii iii
per iv
The
Intercept:
g.) Create a well labeled scatterplot of this data, insert trendline and display equation.
f.) Looking at the scatterplot it appears that the U.S. population is growing linearly from 1950 to 2010. Transform these years to Years since 1950 by entering a formula in the appropriate cells.
h.) Using the second scatterplot, type in the slope and 𝑦𝑦-intercept from the equation without using scientific notation. Format with commas and no decimal places.
i.) Now use the built-in SLOPE and INTERCEPT functions to find exact values for these constants using the data from 1950 to 2010. Format to zero decimal places.
j.) Enter a formula that uses the values from part i for the 1950 to 2010 data to predict the U.S. population in 2050. Format with commas and no decimal places.
i
is changing by
ii iii
per
iv
.
k.) Interpret the SLOPE value in a sentence by filling in the blanks in the sentence below.
The ___i____ is changing by ____ii_____ ___iii____ per __iv___.

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