SOLUTION: For every 3 degree rise in temperature, the volume of a certain gas expands by 4 cubic centimeters. If the volume of the gas is 24 cubic centimeters when the temperature is 32 degr

Question 1094465: For every 3 degree rise in temperature, the volume of a certain gas expands by 4 cubic centimeters. If the volume of the gas is 24 cubic centimeters when the temperature is 32 degrees, what was the volume of the gas in cubic centimeters when the temperature was 20 degrees?
I was able to figure out the answer to this problem through a process which did not involve any equations. I was wondering if someone could help me put this problem into equation form. The answer is 8.
Thank you so much for your help.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
volume of gas is 24 cubic centimeters when the temperature is 32 degrees.
for every 3 degree rise in temperature, the volume of gas expands 4 cubic centimeters.
conversely for every 3 degrees fall in temperature, the volume of gas contracts 4 cubic centimeters.
difference between 32 and 20 is 12 degrees.
for every 3 degrees, volume of gas contracts 4 centimeters.
12/3 = 4
4 * 4 = 16
volume of gas drops from 24 to 8.

you got it right.

how to solve in equation form:

let x = number of degrees.
let y = number of cubic centimeters.

slope intercept form of the equation of a straight line is y = mx + b

m is the slope
b is the y-intercept.

you know that for every change of 3 degrees, the volume of gas changes 4.

your slope is change in y divided by change in x.

your slope should therefore be 4/3

y = mx + b becomes y = 4/3 * x + b

to solve for b, you take any one point on the line and replace x and y with it and then solve for b.

one of your points is given as (32,24)

the format of the point is (x,y).

therefore, when x = 32, y = 24.

replace x with 32 and y with 24 in the equation of y = 4/3 * x + b and you get:

24 = 32 * 4/3 + b

solve for b to get b = -56/3

your equation should be:

y = 4/3 * x - 56/3

when x = 32, y = 4/3 * 32 - 56/3 = 24

when x = 20, y = 4/3 * 20 - 56/3 = 8

equation looks good.

here's what the graph looks like:

$$$

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