Question

Kinda stuck on this............

I have figured out part (a) in this problem, it is the rest I don't know anything about.

The yearly production of a 6 foot orange tree is 20 pounds of
oranges. A 16 foot tree produces 58 pounds. Let H represent
the height of an orange tree and p the number of pounds of
oranges produced. Use the information to answer the questions
shown below.

(a) What is the ordered pair for the first tree?
(6,20)

What is the ordered pair for the second tree?
(16,58)


(b) Find the point-slope form of an equation of the line
through the two ordered pairs.

Possible Answers (multiple choice):

A. p-20=19/5(h-6)

B. p=19/5h - 14/5

C. p-20=-19/5(h-6)

D. p-6=5/19(h-20)

(c) Use the equation from part (b) to predict the number
of pounds of oranges produced by an 18 foot tree; a 20 foot
tree.

What is the predicted production of an 18 foot tree?
(Round to the nearest whole number)

What is the predicted production of a 20 foot tree?
(Round to the nearest whole number)

(d) Use the equation from part (b) to predict the height of a tree
which produces 88 pounds of oranges.

What is the predicted height (in feet) of a tree that
produces 88 pounds of oranges?
(Round to the nearest tenth)

Answer 1

points are \((6,20)\) and \((16,58)\) slope is
\[m=\frac{58-20}{16-6}=\frac{38}{10}=\frac{19}{5}\]

Answer 2

Find the point-slope form of an equation of the line through the two ordered pairs.
\[y-y_1=m(x-x_1)\]in your case
\[p-20=\frac{19}{5}(h-6)\]

Answer 3

So the same thing would happen with part c, but the (h-6) would be (h-18) instead and where the 20 is would be x?

Answer 4

I just started understanding the y=mx+b formula, so this one for the point-slope I know nothing about.

Answer 5

oh no hold on

Answer 6

What is the predicted production of an 18 foot tree? (Round to the nearest whole number)
replace \(h\) by \(18\) and solve for \(p\)

Answer 7

\[p-20=\frac{19}{5}(h-6)\]with \(h=18\) becomes
\[p-20=\frac{19}{5}(18-6)\]
\[p-20=\frac{19}{5}\times 12\]
\[p=\frac{19}{5}\times 12+20\] whatever that is is your answer

Answer 8

p = 328 over 5.

Answer 9

you could write this in slope intercept form if you like

Answer 10

says to round to the nearest whole number

Answer 11

i would use a calculator and use \(3.8\) for \(\frac{19}{5}\)

Answer 12

\[3.8\times 12+20=65.6\] according to my calculator, so maybe they want you to say 66

Answer 13

Ok, so switch the 19 over 5 to decimal.

Answer 14

that is what would do since i don't really want to add all those fractions, and you have to round in any case

Answer 15

So the next answer for the 20 foot tree would be 73?