Question

I have a word problem involving a linear equation. I have an idea on how to do it, but got stuck. please help.

Answer 1

a candle is 17in tall after burning for 3 hours.
it becomes 15in tall after burning for 5 hours.
I have to write a linear equation and then predict how tall it is after 8 hours.

Answer 2

I started with using slope formula which is m=y2-y1/x2-x1

Answer 3

where did you get so far?

Answer 4

I got m=5-3/15/17 and got 2/-2

Answer 5

i mean 15-17

Answer 6

You can use the slope - point form after that.

Answer 7

I did, and got y-5=-2/2(x-15) and that's where i got stuck. I know I have to simplify it but the fraction is confusing me

Answer 8

Okay. First of all, y refers to the height of the candle and x refers to the time.

So, at x = 3 hours, y = 15 in.

=> (y - 15) = -1(x - 5)

Answer 9

I thought since (15,5) 5 is y1 and 15 is x1

Answer 10

Oh, sorry. My mistake. I assumed that you had taken it the other way. Okay. So, yeah - (15, 5) is a point on the line. So,

(y-5) = - 1(x-15)
y - 5 = 15 - x
x + y - 20 = 0

Answer 11

I just didn't simplify the fraction into -1, that's what messed me up. let me work out the problem and tell you what I got. (for the question of how tall will the candle be after burning for 8 hours. )

Answer 12

Yeah, sure. Take your time.

Answer 13

wait, how did you get x+y-20=0? when I simplified I had y-5=15-x and then added 5 to both sides and got y=15-5x

Answer 14

If you add 5 to both sides,

y - 5 + 5 = 15 - x + 5
y = 20 - x

Answer 15

and I use that as the equation to find how tall it will be after 8 hours?

Answer 16

Yup. So you plug in x = 8 and you find the y value corresponding to that.

Answer 17

So, after 8 hours the candle will be 12in. tall.

Answer 18

Yup. :)

Answer 19

Thank you so much!