Question

a candle has been burning for 20 min and is now 25 cm tall. in an hour it will be 10 cm tall. which equation models the height of the candle y in cm, x minutes after it was lit?
a ( y - 25 = -4(x - 20) )
b ( y - 25 = -\frac{3}{8}(x - 20) )
c ( y + 25 = -0.25(x + 20) )
d ( y - 25 = -0.25(x - 20) )

Explanation:

Step1: Identify two points

We have two points: when \( x = 20 \) (20 minutes after being lit), \( y = 25 \) cm; and when \( x = 20 + 60=80 \) (1 hour = 60 minutes later, so 80 minutes after being lit), \( y = 10 \) cm. So the two points are \( (20, 25) \) and \( (80, 10) \).

Step2: Calculate the slope

The slope \( m \) between two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting \( (x_1,y_1)=(20,25) \) and \( (x_2,y_2)=(80,10) \), we get \( m=\frac{10 - 25}{80 - 20}=\frac{- 15}{60}=- 0.25 \).

Step3: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We use the point \( (20,25) \) and \( m=-0.25 \). Substituting these values into the point - slope formula, we get \( y - 25=-0.25(x - 20) \).

Answer:

D. \( y - 25=-0.25(x - 20) \)