lines section

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
7
hours of burning, a candle has a height of
28.3
centimeters. After
24
hours of burning, its height is
26.6
centimeters. What is the height of the candle after
14
hours?

Answer 1

height is a function of time.

x axis is time in hours

y axis is height in cm

 

We have two points on the line: (7, 28.3), (24, 26.6)

 

To find the equation of the line 1st find the slope:

m = (26.6-28.3)/(24-7) = -0.1

 

The slope intercept form is  y = mx + b where m=slope, b = y-intercept

 

y = -0.1x + b

Plug in one of the given points for (x,y) and solve for b

 

28.3 = -0.1(7) + b

28.3 = -0.7 + b

29 = b

 

The equation of the line is y = -0.1x + 29

Note:  This equation tells us the candle was initially 29 cm tall and loses 0.1 cm per hour height when burnt.

 

To find the height after 14 hours plug in 14 for x and solve for y

 

y = -0.1(14) + 29

y = 27.6 cm