Find the expression.

Question

on Saturday Alberto filled his right rear tire with air at the gas station around the block from where he lives. Three days later the tire pressure in that tire measured 26 PSI. On the following Saturday one week after he had originally filled the tire, the tire pressure measured 18 PSI. Assume that the tire has been losing tire pressure at a constant rate since he filled the tire. Find the expression.

Answer 1

To solve this problem you need need to write a linear function. A linear function can be written of the form y=mx+b.

Define your information. Use the number of days in a week and the tire pressures as points.
day 3    3=x1 and 26=y1
day 7    7= x2 and 18=y2

First find the slope.

To find slope use the formula:
m = (y1-y2)/(x1-x2)

Substitute:
m = (26-18)/(3-7)

Simplify:
m=(8/(-4))=-2

Now you have the function y=-2x+b.

To be sure the function includes the data points, plug in one of the coordinates and solve for b. (So either x1,y1 or x2,y2)

Choose x1,y1 and substitute

y=3.65x+b.
26=-2(3)+b
26=-6+b
20=b

Plug the value b into the linear function y=-2x+b.

Therefore, a linear function is y=-2x+20.

To check plug in the x2, and you should get y2. (It checks)

 

The expression then is -2x+20.

Answer 2

Let y = the tire pressure and x equal the days since Alberto filled the tires.  We have two points, (3,26) and (7,18), which is all we need to find the equation of the line, y = mx + b, where m is the slope and b is the y-intercept.  The formula for the slope is:

 

m = (y₂-y₁)/(x₂-x₁)

 

where (x₁,y₁) and (x₂,y₂) are two points on the line.  Plug in in the values from the two points we have:

 

m = (18-26)/(7-3) = -8/4 = -2

 

So the equation of the line so far is:

 

y = -2x + b

 

To find b, plug in the x and y values from either of the two known points.  I'll use (3,26):

 

26 = -2*3 + b

26 = -6 + b

32 = b

 

y = -2x + 32