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. I have a bit of an idea how to do this but the format requires that I be very detailed to get full points. Please help! Thanks.

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. I have a bit of an idea how to do this but the format requires that I be very detailed to get full points. Please help! Thanks.

anonymous · Answer

height, h,   and time, t,   are like y and x in equations you've probably seen before.

So you have two ordered pairs of (x,y), but they are expressed as (t, h).

If you have two ordered pairs, can you recall how to write a linear equation (i.e. equation for a line)?

anonymous · Answer

y=mx+b i believe?

anonymous · Answer

oh gosh i closed this question already didn't I well, I opened a new one and still need a little help with that one x.x

anonymous · Answer

I think you will need to find the slope...

m = (y2 - y1) / (x2 - x1)    

here, using (t, h) points, slope would be (h2 - h1) / (t2 - t1)

anonymous · Answer

So, step 1 is to use the two (t,h) points given in the problem and find the slope.

Then you can use the slope, m, and one of the points to set up the linear equation.

h - h1 = m(t - t1)     <<----- plug in the slope you found and one of the (t,h) points
                                                then simplify

anonymous · Answer

oh I see! so.. hm I really wished I hadn't closed this haha. so plug in like 5 and 15.  to the slope. And to find where it would be at 8 hours..? plug in 8 and..