Laura weighed 130 lbs. in 1986 and weighed 175 lbs. in 2007. Express the given information in this problem as two-ordered pairs. (1986, 130 ) and ( 2007 175 ) At what rate is this person's weight increasing each year? Include units in your answer. Round your answer to the nearest hundredth. If this person's weight gain continues at this same rate, in what year will they weigh at least 200 lbs.?
Part A
Find out the unit rate or slope of the linear equation
we have the points
(1986, 130 ) and ( 2007 175 )
m=(175-130)/(2007-1986)
m=45/21
m=2.14 lb per year
Part B
If this person's weight gain continues at this same rate, in what year will they weigh at least 200 lbs
step 1
Find the equation of the linear equation
y=mx+b
we have
m=2.14
point (1986,130)
substitute
130=2.14(1986)+b
solve for b
b=130-4,250.04
b=-4,120.04
therefore
y=2.14x-4,120.04
For y=200 lbs
substitute
200=2.14x-4,120.04
solve for x
2.14x=200+4,120.04
2.14x=4,320.04
x=2,019
therefore
the answer is
year 2019