Question

A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the candlestick is 13.4 inches tall. Write and solve a linear equation to find the original height of the candle.

Answer 1

The original height of the candle is 15 inches

Explanation:

Let

x ----> the number of hours

y ----> the height of the candlestick

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or the unit rate of the linear equation

b is the y-intercept or initial value of the linear equation

In this problem we have

The slope is equal to
`m=-0.2\ (in)/(h)`

Is negative because is a decreasing function

we have the ordered pair (8,13.4)

substitute in the equation

`13.4=-(0.2)(8)+b`

solve for b

Note: In this context the y-intercept is equal to the original height of the candle

`13.4=-1.6+b`

`b=13.4+1.6`

`b=15\ in`

therefore

`y=-0.2x+15`