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Answer:

The slopes of line segments AC and AD are same or constant i.e [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

We need to find slopes of AC and AD and tell if they are same or not.

The formula used to calculate slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Finding slope of AC

We have A=(3,2) and C=(0,1)

Finding slope using formula:

We have [tex]x_1=3, y_1=2, x_2=0,y_2=1[/tex]

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{1-2}{0-3}\\Slope=\frac{-1}{-3}\\Slope=\frac{1}{3}[/tex]

So, Slope of AC is [tex]\frac{1}{3}[/tex]

Finding slope of AD

We have A=(3,2) and C=(9,4)

Finding slope using formula:

We have [tex]x_1=3, y_1=2, x_2=9,y_2=4[/tex]

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{4-2}{9-3}\\Slope=\frac{2}{6}\\Slope=\frac{1}{3}[/tex]

So, Slope of AD is [tex]\frac{1}{3}[/tex]

So, the slopes of line segments AC and AD are same or constant i.e [tex]\frac{1}{3}[/tex]

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An 8-column table with 14 rows titled Table 1, Employment by major industry sector, 1996, 2006, and projected 2016. Column 1 is labeled Industry sector with entries services-providing, utilities, wholesale trade, retail trade, transportation and warehousing, information, financial activities, professional and business services, educational services, health care and social assistance, leisure and hospitality, other services, federal government, state and local government. Column 2 is thousands of jobs in 1996 with entries 97,042.9, 639.5, 5,522.1, 14,142.6, 3,935.5, 2,940, 6,968.6, 13,461.8, 2,077.5, 11,604.8, 10,776.5, 5,434.9, 2,877, 16,662.1. Column 3 is labeled thousands of jobs in 2006 with entries 114,407.3, 548.5, 5,897.7, 15,319.4, 4,465.8, 3,054.9, 8,363.2, 17,551.6, 2,918.4, 14,919.8, 13,143.4, 6,234.6, 2,728.3, 19,261.7. Column 4 is labeled thousands of jobs in 2016 with entries 130,189.7, 517.6, 6,326.2, 16,006.4, 4,962, 3,266.7, 9,570.1, 21,643.7, 3,527.4, 18,954.1, 15,016.7, 7,077.2, 2,625.7, 20,696.1. Column 5 is labeled Numeric change 1996 to 2006 with entries 17,354.4, negative 91, 375.6, 1,176.8, 530.3, 114.9, 1,394.6, 4,089.8, 840.9, 3,315, 2,366.9, 799.7, negative 148.7, 2,599.6. Column 6 is labeled numeric change 2006 to 2016 with entries 15,782.4, negative 30.9, 428.5, 687, 496.2, 211.8, 1,206.9, 4,092.1, 609, 4,034.3, 1,873.3, 842.6, negative 102.6, 1,434.4. Column 7 is labeled Average annual rate of change, 1996 to 2006 with entries 1.7, negative 1.5, .7, .8, 1.3, .4, 1.8, 2.7, 3.5, 2, 1.4, negative .5, 1.5. Column 8 is labeled average annual rate of change, 2006 to 2016 with entries 1.3, negative .6, .7, .4, 1.1, .7, 1.4, 2.1, 1.9, 2.4, 1.3, 1.3, negative .4, .7. Based on the above chart, which industry’s average annual rate of change is projected to decrease the most in the 2006-2016 period as compared to its average annual rate of change during 1996-2006? a. Utilities b. Educational services c. Federal government d. State and local government