J is filling his gas tank. After 10 seconds, his gas tank has 5 gallons in it. After 25 seconds, his tank has 9.5 gallons. Suppose the amount of gas in the tank depends linearly on time. Write and equation describiing the gallons of gas in the tank g after s seconds. How much gas will be in the tank after 50 seconds? What does this number mean in the problem? My equation looked like this; 10x+5y=50 I then found the x and y intercept independently getting (5,0) and (0,10) and as far as the y intercept that is where the line crosses over the y axis. Does this sound totally wrong or are parts correct?

## Could someone tell me if this is correct?

# 2 Answers

Great job by Kevin.

Here is a way with more physics meaning.

Let G be the amount of gas in the tank at time t. Since at t = 10, G = 5, and t = 25, G = 9.5, the amount of gas increased 9.5-5 = 4.5 gal in 25-10 = 20 sec.

Therefore, at time t, G can be writen as,

G = (4.5/15)(t-10) + 5

Answer: G = 0.3t + 2, gal

One approach is to first determine the slope. If we base our points on (time, gallons), we get the two points (10,5) and (25, 9.5)

Using these, we can determine the slope using m = (y2 - y1)/(x2 - x1) , or

m = (9.5 - 5)/(25 - 10) = 0.3

Put this and a point into the point slope form (y - y1) = m(x - x1) to determine the equation:

y - 5 = 0.3 (x - 10)

y - 5 = 0.3x - 3

y = 0.3x + 2

So J's tank initially had 2 gallons of gas in it.

NOTE: Since the equation should be expressed in terms of s (seconds) and g (gallons), it should look like this:

g = 0.3s + 2

We can then use the equation to deteremine the amount of gas at s=50:

g = 0.3(50) + 2

g = 15 + 2 = 17 gallons at 50 seconds