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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.

Respuesta :

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

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 [tex]t[/tex] and the height is [tex]h[/tex], then two points in form of [tex](t,h)[/tex] will be:  [tex](3, 17)[/tex] and [tex](5, 15)[/tex]

Now slope [tex]=\frac{15-17}{5-3}=-\frac{2}{2}=-1[/tex]

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

Plugging the point [tex](3, 17)[/tex] into the above equation........

[tex]17=-1(3)+b\\ \\ 17=-3+b\\ \\ 17+3=b\\ \\ b=20[/tex]

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

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

[tex]h=-8+20\\ \\ h=12[/tex]

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

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