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Question 1083926: In 2005, the percent of U.S. drivers wearing seat belts was 82%. The number of drivers
wearing seat belts in 2000 was 71%. Let y be the number of drivers wearing seat belts
in the year x where x = 0 represents the year 2000.
a) WritealinearequationthatmodelsthepercentofU.S.driverswearingseatbeltsinterms
of the year x.
b) Use the equation foundin part(a)topredictthe percentage ofU.S. driverswearing seat
belts in the year 2014.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the percent of us drivers wearing seat belts in 2005 was 82%.
the percent of us drivers wearing seat belts in 2000 was 72%.
the difference between the percent in 2005 and the percent in 2000 is 82 - 72 = 10%.
the percent difference per year would be 10% / 5 = 2%.
2% is your slope.
the slope intercept form of a straight line is y = mx + b
m is the slope and b is the y-ingtercept.
when m is the change in the percent per year which is equal to 2.
the general formula becomes y = 2x + b
to find the y-intercept, replace x and y with the value from one of the points.
if you assume that x = 0 represents the year 2000, then:
x = 5 represents the year 2005, and:
x = 14 represents the year 2014.
one of your data points would be the percent in the year 2005.
that point would be (x,y) = 5,82
the formula of y = 2x + b becomes 82 = 2 * 5 + b
simplify to get 82 = 10 + b
solve for b to get b = 72
your y-intercept is 72
your slope intercept formula becomes y = 2x + 72
your y-intercept is the value of y when x = 0.
the graph of your equation would look like this:
the blue line is the graph of the equaiton.
the orance lines are just there to allow me to show you what the intersection points are.
when x = 0, y = 72
when x = 5, y = 82
when x = 14, y = 100
x = 0 represents the year 2000.
x = 5 represents the year 2005.
x = 14 represents the year 2014.
the value of y is in percent format, i.e. y = 72 means that y = 72%.
you can see that the formula accurately represents the data points given, assuming a linear equation which give you straight line growth.
when x = 0, you have 72% in 2000.
when x = 5, you have 82% in 2005.
the value of y = 100% when x = 14 is the extrapolation from the formula.
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