Suppose that the height (in centimeters) of a candle is a linear function of the amount of time

Question

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 14 hours of burning, a candle has a height of 15 centimeters. After 25 hours of burning, its height is 9.5

 centimeters. What is the height of the candle after 20  hours?

Answer 1

14 hours h=15 cm

25 hours h = 9.5

20 hours 9.5<h<15

20 is closer to 25 than to 14, so h is closer to 9.5 than 15

it's 5/(25-14) x (15-9.5) = 5/11x5.5 =5x.5= 2.5

add 2.5+9.5 = 12

h=12 cm in 20 hours

or

plot the 2 points on a graph, (h,t)= (14,15) and (25, 9.5). line through them has slope

= "rise over run"

= change in y over change in x

= (15-9.5)/(14-25)=

-5.5/11=-.5=

-1/2= (y-15)/(x-14)

y is the height of the candle, x=hours the candle burned

y-15=-.5(x-14)

y= -.5x +22

y(20) = -.5(20) +22 = -10+22

= 12 cm after 20 hours

y(14)=-.5(14)+22 =15 cm after 15 hours

y(25)=-.5(25)+22= 9.5 cm after 25 hours