Question

The height (in centimeters) of a candle is a linear function of the amount of time in hours) it has been burning. When graphed, the function gives a line with aslope of -0.5. See the figure below.Suppose that the height of the candle after 17 hours is 16.5 centimeters. What was the height of the candle after 13 hours?

Answer 1

From the question

The slope of the graph is

$m\text{ = -0.5}$

using the equation of a line

$y\text{ = mx + c}$

we can find the intercept C, where m is the slope of the line

From the question,

the height of the candle after 17 hours is 16.5 centimeters implies

$\begin{gathered} x\text{ = 17 hours} \\ y\text{ = 16.5cm} \end{gathered}$

Using this information we can get the intercept C.

Substitute the values of x, y and m into the equation of line

$\begin{gathered} \text{x = 17, y = 16.5 , m = -0.5 } \\ y\text{ = mx + c} \\ 16.5\text{ = -0.5(17) + C} \\ 16.5\text{ = -8.5 + C} \\ 16.5\text{ + 8.5 = C} \\ C\text{ = 25} \end{gathered}$

Now we need to find the height of the candle after 13hours

therefore, x = 13, m = -0.5, C = 25

$\begin{gathered} y\text{ = mx + c} \\ y\text{ = -0.5(13) + 25} \\ y\text{ = -6.5 + 25} \\ y\text{ = 18.5} \end{gathered}$

Therefore,

The height of the candle after 13hours is 18.5 centimeters