Acandlestick 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.

The original height of the candle is 15 inches

Step-by-step 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

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

Is negative because is a decreasing function

we have the ordered pair (8,13.4)

substitute in the equation

solve for b

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

therefore

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: