A study in 2000 by the National Highway Traffic SafetyAdministration estimated t

Question

A study in 2000 by the National Highway Traffic SafetyAdministration estimated that failure to wear the seat belts led to9200 deaths in the previous year, and that the number of deathswould decrease by 270 for every 1 percentage point gain in seatbelt usage. Let y = predicted number of deaths in a year and x =percentage of people who wear seat belts

a) Report the slope b for the equation y = a + bx

b) If the y intercept equals 28,910, then predict the number ofdeaths in a year if ....

(i) no one wears seats belts
(ii) 73 % of people wear seat belts ( the value in 2000 )
(iii) 100 % of people wear seat belts

Explanation / Answer

Slope, if you remember from a general algebra class, is changein y over change in x. The slope here is given to you right inthe problem, “the number of deaths would decrease by 270 forevery 1 percentage point gain in seat beltusage.” Therefore, your slope is -270 (negative becauseit says number of deaths would DECREASE). If your y-interceptis 28,910, your equation is y = 28910 – 270x where x is thepercentage of people who wear their seat belts. To find yournext three answers, we simply plug the numbers given in for x inour equation. So,

(i)   no one wears seat belts: y = 28910 –(270*0) = 28910 deaths

(ii)  73% of people wear seat belts: y = 28910 –(270*73) = 9200 deaths (which was also given to you in the originalproblem since the x given was for the year 2000)

(iii) 100% of people wear seat belts: y = 28910 –(270*100) =1910 deaths

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