Question

A candle burned at a steady rate. After 38 minutes, the candle was 11.2 inches tall. Eighteen minutes later, it was 10.75 inches tall. Use an equation in point-slope form to determine the height of the candle after 4 hours. Round the answer to the tenth place if necessary.

Answer 1

Let us take time by x variable and height of the candle by y variable.

We can setup two coordinates form the given statements:

After 38 minutes, the candle was 11.2 inches tall : (38, 11.2)

Eighteen minutes later, it was 10.75 inches tall : (56,10.75).

We need to write slope -intercept form of the equation first.

Slope-intercept form is :

y-y1 = m(x-x1).

In order to find slope-intercept form we need to find the slope of the given equation.

Slope between (38, 11.2) and (56, 10.75) points :

$m=\frac{10.75-11.2}{56-38}$

$m=-0.025$

Let us apply slope-intercept form y-y1 = m(x-x1).

y- 11.2 = -0.025 (x-38)

Now, we need to find the height of the candle after 4 hours.

We took time in minutes.

Therefore, 4 hours = 4× 60 = 240 minutes.

In order to find the height of the candle after 4 hours, we need to plug x=240 in above slope-intercept form.

y- 11.2 = -0.025 (240-38)

y-11.2 = -0.025 ( 202)

y-11.2 = -5.05

Adding 11.2 on both sides, we get

y-11.2+11.2 = -5.05+11.2

y = 6.15

We need to round it to the tenth place.

Therefore, y = 6.15.

Therefore, the height of the candle after 4 hours is 6.15 inches.