SOLUTION: 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

Algebra ->  Square-cubic-other-roots -> SOLUTION: 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      Log On


   

Question 1042509: 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 by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plot tree diameter on the vertical axis and
time in years on the horizontal axis
-------------------
You are given 2 point on the line:
( 1,4 )
( 10,25 )
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Use the general point-slope formula
+%28+y+-+4+%29+%2F+%28+x+-+1+%29+=+%28+25+-+4+%29+%2F+%28+10+-+1+%29+
+%28+y+-+4+%29+%2F+%28+x+-+1+%29+=+21+%2F+9+
+%28+y+-+4+%29+%2F+%28+x+-+1+%29+=+7+%2F+3+
Multiply both sides by +%28+x-1+%29%2A3+
+3%2A%28+y+-+4+%29+=+7%2A%28+x+-+1+%29+
+3y+-+12+=+7x+-+7+
+3y+=+7x+%2B+5+
+y+=+%287%2F3%29%2Ax+%2B+5%2F3+
-----------------------
check the answer:
does the line go through
( 1,4 )
( 10,25 ) ?
------------
+y+=+%287%2F3%29%2Ax+%2B+5%2F3+
+4+=+%287%2F3%29%2A1+%2B+5%2F3+
+4+=+7%2F3+%2B+5%2F3+
+4+=+12%2F3+
+4+=+4+
and
+y+=+%287%2F3%29%2Ax+%2B+5%2F3+
+25+=+%287%2F3%29%2A10+%2B+5%2F3+
+25+=+70%2F3+%2B+5%2F3+
+25+=+75%2F3+
+25+=+25+
OK