Question

Extra points!! A candle is 17 in tall after burning for 3 hours. After 5
hours, it is 15 in, tall. Write a linear equation to
model the relationship between heighth of the candle and time t. Predict how tall the candle will be after burning 8 hours? Please show your steps and explain your work:))
Everything helps!! Thank you so much in advance!!

Answer 1

Answer:

1) $h=-t+20$  

2) 12 inches tall.

Step-by-step explanation:

1) The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

In this case:

$y=h$ (The height of the candle in inches)

$x=t$ (The time in hours)

Then, we can rewrite it:

$h=mt+b$

Based on the information provided in the exercise, the line passes through these points:

$(3,17)$ and $(5,15)$

Then, we can find the slope of the line with the formula $m=\frac{y_2-y_1}{x_2-x_1}$:

 $m=\frac{15-17}{5-3}=-1$

Now we need to substitute the slope and one of the points into  $h=mt+b$  and then solve for "b":

$17=(-1)(3)+b\\\\b=17+3\\\\b=20$

Substituting values, we get that the a linear equation that models the relationship between the heigth of the candle and the time, is:

$h=-t+20$  

2) We must substitute $t=8$ into the linear equation  $h=-t+20$ in order to find the height of the candle after burning 8 hours:

 $h=-(8)+20\\\\h=12$