Exercise 18 Page 211

Remember to express 2 hours in minutes when calculating the height of the candle.

9 inches

Practice makes perfect

We will first write the equation in point-slope form and later use it to calculate the height of the candle after 2 hours.

Write the equation

In order to write the equation in point-slope form, we need to know the slope m and a point which lies on the line (x_1,y_1). y-y_1=m(x-x_1)To calculate the slope, we need two points that solve the equation. We are told that, after 32 minutes, the candle was 11.2 inches tall. Therefore, the first point is (32,11.2). It is also given that 18 minutes later, or after 50 minutes of burning, it was 10.75 inches tall. Thus, the second point is (50,10.75). Let's substitute these into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 32,11.2) & ( 50,10.75)

m=10.75- 11.2/50- 32

SubTerms

Subtract terms

m=- 0.45/18

MoveNegNumToFrac

Put minus sign in front of fraction

m=- 0.45/18

UseCalc

Use a calculator

m=- 0.025

To write the equation, we can substitute the value of the slope and one of the points, let's take ( 32, 11.2), into the point-slope form. y- 11.2=- 0.025(x- 32)

Calculate the Height

We want to determine the height of the candle after 2 hours of burning. In our equation, x represents the number of minutes passed so we need to express 2 hours in minutes. 2* 60=120minutes Now, we can substitute 120 for x and solve for y, which represents the height of the candle in inches.

y-11.2=- 0.025(x-32)

Substitute

x= 120

y-11.2=- 0.025( 120-32)

SubTerm

Subtract term

y-11.2=- 0.025( 88)

Multiply

y-11.2=- 2.2

AddEqn

LHS+11.2=RHS+11.2

y=9