SOLUTION: A candle is 8 in. tall after burning 2 hrs. After 4 hrs it is 5 1/2 in. tall. Write a linear equation to model the height y of the candle after x hours. After how many hours wil

Algebra ->  Linear-equations -> SOLUTION: A candle is 8 in. tall after burning 2 hrs. After 4 hrs it is 5 1/2 in. tall. Write a linear equation to model the height y of the candle after x hours. After how many hours wil      Log On


   

Question 814097: A candle is 8 in. tall after burning 2 hrs. After 4 hrs it is 5 1/2 in. tall. Write a linear equation to model the height y of the candle after x hours. After how many hours will the candle be 4 inches tall?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The description gives two data points, (x,y) where x is time and y is tallness of the candle. These two points are (2, 8) and (4, 5.5). These two points define a line in variables x and y.

That desired line:
All using slope-intercept form, m=%285.5-8%29%2F%284-2%29=-2.5%2F2=-5%2F4;
y=mx%2Bb
b=y-mx
Use either point from the problem description,
b=8-%28-5%2F4%29%2A2
b=8%2B%285%2F4%29%2A2
b=8%2B5%2F2=8%2B2.5
b=10.5

The equation for the line is highlight%28y=%285%2F4%29x%2B10%261%2F2%29;
Again, y is tallness or height of the candle in inches, and x is time in hours after burning (at the wick). The question is about how much time to burn to become 4.5 inches. JUST SOLVE THE EQUATION FOR x, and let y=4.5.

The whole situation could have been analyzed using x for tallness and y for burn time, but normally, most people would use time as an independant variable and something else as the dependant variable.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A candle is 8 in. tall after burning 2 hrs. After 4 hrs it is 5 1/2 in. tall. Write a linear equation to model the height y of the candle after x hours. After how many hours will the candle be 4 inches tall?

Linear equation: highlight_green%28y+=+%28-+5%2F4%29x+%2B+21%2F2%29, with x being time (in hours), and y being height

After substituting 4 for y in the above linear equation, it's seen that it'll take highlight_green%285.2%29 hours, or highlight_green%285_hours_12_minutes%29 to reach 4".

You can do the check!!

Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com. Further help is available, online or in-person, for a fee, obviously.

For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams, GENERAL MATH QUESTIONS, MATH HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra, Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE, GRE, CLEP, and the GED, you can visit: http://asvabstudyzone.freeforums.net/.