Question

Sshow all the steps that you use to solve this problem in the space provided.

A candle is 17 in. tall after burning for 3 hours. After 5 hours, it is 15 in. tall. Write a linear equation to model the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8 hours.

Answer 1

For begining mark:

x = the time in hours

y = the height in inches

You know:

A candle is 17 in tall after burning for 3 hours.

After 5 hours, it is 15 in tall.

This mean x1 = 3h , y1 = 17in , x2 = 5h , y2 = 15 in

Find the slope m of the linear equation between this two points.

m = ( y2 - y1 ) / ( x2 - x1 )

substitutes the values

m = ( 15 - 17 ) / ( 5 - 3 ) = - 2 / 2 = - 1

The equation of the line in the point-slope form is:

y - y1 = m ∙ ( x - x1 )

so

y - 17 = ( - 1 ) ∙ ( x - 3 )

y - 17 = - x + 3

Add 17 to both sides

y - 17 + 17 = - x + 3 + 17

y = - x + 20

Replace y with h and x with t

h = - t + 20

For predicting put t = 8 into you equation

h = - t + 20 = - 8 + 20 = 12

After burning 8 hours tall the candle will be 12 in