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 8 hours.

Answer 1

so can you find the slope

the 2 points are (3, 17) and(5, 15)

Answer 2

once you know the slope use the slope point formula to get the equation of the line.

Answer 3

the slope is -1

Answer 4

great so you have a point (3, 17) and slope of -1

so the equation is

y = -x + b

substitute y = 17 and x = 3 to find b

Answer 5

you many need to write it as

h = -t + b

and b is the y intercept or initial height

Answer 6

@campbell_st i dont get it

Answer 7

ok... so if you use the point slope formula

\[y - y_{1} = m(x - x_{1})\]

using m = -1 and (3, 17)

y - 17 = -1(x - 3)

y - 17 = -x + 3

now you should be able to find the equation

Answer 8

if you use the slope intercept form of a line

y = mx + b

or using the slope m = -1

y = -x + b

you have a point and slope

17 = -1(3) + b

so b = 20

so the equation is

y = -x + 20

so just substitute x = 8 to find the height after 8 hours

Answer 9

since the -x is a negative should the 8 be negative as well