Question

A candle is 18 in. tall after burning for 3 hours. After 5 hours, it is 16.5 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

Answer: 12 inches After 8 Hours

Step 1

Find the slope m of the linear equation between points A and B

we know that

The formula to calculate the slope between two points is equal to

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

substitutes the values

M=((15-17)/((5-3)))

M= (-(2)/((2)))

M= -1

Step 2

Find the equation of the line

we know that

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

y-y1=m*(x-x1)

we have

m=-1

A(3,17)

substitute in the equation

y-17=-1*(x-3)

y=-x+20--------> this is the linear equation that model the relationship between height h of the candle and time t

Step 3

Find the height for x=8 hours

substitute the value of x in the linear equation

y=-8+20

y=12 Inches

The height of the candle will be 12 inches after 8 Hour