Year19701980199020002010Hours20201880173016901570 The table to the right lists the annual hours worked by the average worker in a country for selected years. a) Let x represent the number of years after 1970. Find a formula in slope-intercept form for a linear function f that models the data. b) Interpret the slope of graph of y=f(x). c) Estimate the annual hours worked in 2018.

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Year19701980199020002010Hours20201880173016901570  The table to the right lists the annual hours worked by the average worker in a country for selected years.  a) Let x represent the number of years after 1970. Find a formula in slope-intercept form for a linear function f that models the data.  b) Interpret the slope of graph of y=f(x).  c) Estimate the annual hours worked in 2018.

Dawn Neal · Accepted Answer

SInce x is number of years after 1970  Thus 1970 is at x1=0,y1=2020  1980→x2=10,y2=1880  Now slopf will be  m=y2−y1x2−x1⇒m=1880−202010−0  m=−14010⇒m=−14  a) Equation will by  y−y1=m(x−x1)  y−2020=−14(x−0)  y−2020=−14x⇒y=−14x+2020  b) Slope is -14  Hours worked decreased, on average 14 houes I year  c) For 2018; x=2018−1970⇒48  y=−14(48)+2020  y=672+2020  y=1348 hour

Toni Scott · Accepted Answer

Since the function is linear. So, suppose that the equation of line is y=mx+c.  Since at x=0 the value of y is y=2020.  2020=m(0)+c  c=2020  Put the value c=2020∈y=mx+c.  y=mx+2020  Since x=10 the value of y is y=1860.  1860=10m+2020  10m=−140  m=−14  Put the value of m=−14∈y=mx+2020.  y=−14x+2020  So, the linear function is f(x)=−14x+2020.  b) Since the slope of line m=−14 is negative. So, it means that annual hour worked by the average worker is decreasing.  c) Since f(x)=−14x+2020.  The annual hours worked in 2014 is f(44).  f(44)=−14(44)+2020  f(44)=−616+2020  f(44)=1404.  The annual hour worked by average worker in 2014 is f(44)=1404.

alenahelenash · Accepted Answer

Substituting these values in normal equation, we get 5a+100b=8890 100a+3000b=167700 ⇒a+20b=1778 (1) a+30b=1677 (2) −10b=101 ⇒b=−10110 from (1) a=1778−20(−10110) a=1980 Now puting values of a and b in y=a+bx⇒y=bx+a y=−10110x+1980 b) Compare the above equation with y=mx+c we get slope =m=−10110 Slope =−10110 c) In 2014, x=2014−1970=44 y=−10110(44)+1980 y=1535610 y=76785hvs=1535.6h

\begin{array}{|c|c|}\hline \text{Year}&1970&1980&1990&2000&2010\\ \hline \text{Hours}&2020&1880&1730

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