Question

PLEASE HELP ALGEBRA 2 QUESTION

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 height (h) of the candle and time (t).
Predict how tall the candle will be after burning 8 hours.

Answer 1

The linear equation is:
`h=-t+20` and the height of the candle after 8 hours will be 12 in.

Step-by-step explanation

A candle is 17 in tall after burning for 3 hours and after 5 hours, it is 15 in tall.

If the time is
`t` and the height is
`h`, then two points in form of
`(t,h)` will be:
`(3, 17)` and
`(5, 15)`

Now slope
`=(15-17)/(5-3)=-(2)/(2)=-1`

So, the equation according to slope-intercept form
`(y=mx+b)` will be:
`h=-1t+b` , where
`b` is the y-intercept.

Plugging the point
`(3, 17)` into the above equation........

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

Thus, the linear equation that models the relationship between height of the candle and time will be:
`h=-1t+20` or
`h=-t+20`

Now, for finding the height of the candle after burning 8 hours, we need to plug
`t=8` into the equation. So.....

`h=-8+20\\ \\ h=12`

Thus, the height of the candle after 8 hours will be 12 in.