Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

# math help?

A farmer finds there is a linear relationship between the number of beanstalks, n, she plants, and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 25 oz of beans. When she plants 38 stalks, each plant produces 21 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.

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• Anonymous
2 months ago

If you just want the answer and don't want to learn anything, you can ask at wolfram alpha.  You do need to know enough math to see that with "number of stalks" as the independent variable and "oz. of beans per plant" as the dependent variable, the line passes through point (30, 25) ["25 oz./plant when 30 stalks planted"] and point (38, 21) ["21 oz./plant wheen 35 stalks planted"].

Then the request at Wolfram Alpha would be "Equation of line through (30,25) and (38,21)":

https://www.wolframalpha.com/input/?i=equation+of+...

I prefer the "make technology your servant, not your master" approach, though, so I notice that the slope is -1/2, since planting 8 more stalks (38 - 30 = 8) yields 4 fewer oz./plant (21 - 25 = -4) and -4 / 8  = -1/2.

From there, it's plugging m=-1/2 into the point-slope formula for line with slope m through point (a,b):

y = m(x - a) + b   ...   or  y = mx + b - ma

Use either (30,25) or (38,21) for the (a,b) point.  It doesn't matter, but I'd pick (30, 25) as easier numbers for mental math.  The mx part is -x/2, and b-ma is 25 - (-1/2)(30) = 25 + 30/2 = 25 + 15 = 40.

• 30 stalks yields 750 oz beans (25oz per stalk = 750oz total)

38 stalks yields 798 oz beans

n = stalks

y = oz beans

m = (n1 - n2)/(y1 - y2)

(30, 750) and (38, 798)

(750 - 798)/(30 - 38) = 6

y = 6n + b

Plug in either value to solve for b

750 = 6(30) + b

570

y = 6n + 570

• Given 2 points (n₁, y₁) = (30, 25) and (n₂, y₂) = (38, 21),

the linear rlationship that gives the yield when n staks are planted is

25 - 21       4       -1

m = ----------- = ----- = -----

30 - 38      -8        2

y - 25 = -½ (x - 30)

y = -½ x + 15 + 25

y = -½ x + 40  .....................ANS 