Question

At Martin Nature Center, the park ranger was showing Mrs. Rhames' class a comparison of a tree's age and the diameter of the tree trunk in inches.

The ranger showed them one oak tree that was 1 year old. It had a trunk diameter of 4 inches. Another oak tree was 10 years old. It had a trunk diameter of 25 inches.

Assuming a linear equation fits the situation, what would be the equation of that line?

Answer 1

If x is the age and y is the diameter of the trunk, write the equation:
ax+b=y

We must solve for a and b with the given information.

If (x, y) is (1, 4), we have:

a+b=4

If (x, y) is (10, 25), we have:

10a+b=25

Multiply the first equation by 10 to get:

10a+10b=40

Subtract the second equation from this to get:

9b=25

Thus b=25/9.  a=4-25/9=11/9, so our equation is 11x/9+25/9=y.