Question 358851
Suppose that the height (in centimeters) of a candle is a linear function of
 the amount of time (in hours) it has been burning.
 After 11 hours of burning, a candle has a height of 23.4 centimeters.
 After 30 hours of burning, its height is 12 centimeters.
 What is the height of the candle after 13 hours?
:
Assign the given values as follows:
x1 = 11; y1 = 23.4
x2 = 30; y2 = 12
:
Find the slope using: m = {{{(y2-y1)/(x2-x1)}}}
m = {{{(12-23.4)/(30-11)}}} = {{{(-11.4)/19}}}
:
Find the equation using the point/slope formula: y - y1 = m(x - x1)
y - 23.4 = {{{-11.4/19}}}(x - 11)
y - 23.4 = {{{-11.4/19}}}x + {{{125.4/19}}}
y = {{{-11.4/19}}}x + {{{125.4/19}}} + 23.4
y = {{{-11.4/19}}}x + {{{125.4/19}}} + 23.4
y = {{{-11.4/19}}}x + {{{125.4/19}}} + {{{444.6/19}}}
y = {{{-11.4/19}}}x + {{{570/19}}}
y = {{{-11.4/19}}}x + 30, is the equation
:
What is the height of the candle after 13 hours?
x = 13
y = {{{-11.4/19}}}(13) + 30
y = {{{-148.2/19}}} + 30
y = -7.8 + 30
y = 22.2 cm after 13 hrs