Question 1169299: For the following exercise, write a linear function to model the given data and make the indicated estimation. See Example 7. (Objective 6)
Suppose that in 2000 there were approximately 502 violent crimes per 100,000 people. Suppose further that in 2009 violent crimes dropped to about 424 per 100,000 people. Using the linear function model, estimate the number of violent crimes in 2021 for a city with a population of 400,000.
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! let 2000=0 and 2009=9
(0, 502)
(9, 424)
slope is -78/9
point slope formula is y-y1=m(x-x1) m slope, (x1, y1) point
y-502=-(78/9)x. (or y-424=-(78/9)(x-9))
y=-(78/9)x+502
in 2021, x=21
so y=-(78/9)*21+502
=-182+502=320 per 100,000 people
expect 1280 violent crimes in city with pop of 400,000
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! in 2000 = 502 violent crimes per 100,000 people.
in 2009 = 424 violent crimes per 100,000 people.
straight line projection to 2021 is indicated.
crime statistics in 2000 = 502 per one hundred thousand people.
crime statistics in 2009 = 424 per one hundred thousand people.
equation of a straight line is y = m * x + b
m is the slope
b is the y-intercept.
to find the slope, take two points on the line and assign them to (x1,y1) and (x2,y1) respectively.
the two points on the line are:
(x1,y1) = (0,502) for the coordinate point in the year 2000.
(x2,y2) = (9,424) for the coordinate point in the year 2009.
slope is equal to (y2 - y1) / (x2 - x1)
that becomes (424 - 502) / (9 - 0) = -78/9 = -8.666666....
the y-intercept is the value of y when the value of x is equal to 0, so that is equal to 502
the straight line equation of y = m * x + b becomes:
y = -8.666666.... * x + 502
when x = 0, y = 502 per one hundred thousand.
when x = 9, y = -8.6666666.... * 9 + 502 = 424 per one hundred thousand.
since x = 0 in the year 2000, then x = 21 in the year 2021.
when x = 21, y = 8.6666666.... * 21 + 502 = 320 per hundred thousand.
the graph of this equation looks like this.
since the population is 400,000, then multiply 320 per hundred thousand by 4 to get 1280 homicides in 2021.
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