SOLUTION: A candle is 8 inches tall after burning for 1 hour. After 3 hours it is 5.5 inches tall. What is the equation in y=mx+b form to model the height "Y" of the candle at time "x"

Question 159298: A candle is 8 inches tall after burning for 1 hour. After 3 hours it is 5.5 inches tall.
What is the equation in y=mx+b form to model the height "Y" of the candle at time "x" ??
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=time elapsed (in hours) and y=height of candle (in inches)

Since the "candle is 8 inches tall after burning for 1 hour", this means that we have the values x=1 and y=8 which is the point (1,8)

Also, the statement "After 3 hours it is 5.5 inches tall" tells us that x=3 and y=5.5 which forms the point (3,5.5)

Now let's find the equation of the line through the points (1,8) and (3,5)

First let's find the slope of the line through the points

and

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Divide

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 8 to both sides.

Combine like terms.

So the equation that goes through the points

and

is

Notice how the graph of goes through the points

and

. So this visually verifies our answer.
Graph of through the points

and

--------------------------------------------------
Answer:

So the equation that models the height "y" at time "x" is

RELATED QUESTIONS
A candle is 8 in. tall after burning 2 hrs. After 4 hrs it is 5 1/2 in. tall. Write a... (answered by josgarithmetic,MathTherapy)

Given that a candle is 13.5 inches tall when it has been burning for 8 hours at a rate of (answered by Alan3354,Edwin McCravy)

I have a work problem: Laura lights a candle in her kitchen. The candle is burning at a... (answered by josgarithmetic,josmiceli,MathTherapy)

A new candle is 8 inches tall and burns at a rate of 2 inches per hour. a. Write an... (answered by Theo)

A new candle is 8 inches tall and burns at a rate of 2 inches per hour. what is the... (answered by dyakobovitch)

What is the expression for: A candle that has been burning for 2 minutes is 8 inches... (answered by ewatrrr)

Suppose that the height (in centimeters) of a candle is a linear function of the amount... (answered by josgarithmetic,Boreal)

Suppose that the height (in centimeters) of a candle is a linear function of the amount... (answered by ikleyn,josgarithmetic)

A candle is lit and the length of the burning candle changes at a constant rate of -1.8... (answered by josgarithmetic,greenestamps)