Question

A farmer notices that there is a linear relationship between the number of bean stalks, n, she plants and the yield, Y. When she plants 2 stalks, each plant yields 70 ounces of beans. When she plants 8 stalks, each plant yields 160 ounces of beans.
Which of these equations correctly represents this situation?

Select the correct answer below:


Y(n)=19n+32

Y(n)=11n+72

Y(n)=11n+48

Y(n)=19n+8

Y(n)=15n+30

Y(n)=15n+40

Answer 1

Answer:

Y(n)=15n+40

Step-by-step explanation:

Lets represent the number of bean stalks she plant by n and

the yield by Y.

It says in the question that when she plants 2 stalks, each plant yields 70 ounces of beans. When she plants 8 stalks, each plant yields 160 ounces of beans.

Which means 2 stalks correspond to 70 ounces and 8 stalks corresponds to 160 ounces we could write the data Mathematically like:

(2 , 70) and (8 , 160) are our coordinates where the x-axis would be n the number of beans stalks planted  and y-axis would be Y the yield in ounces.

So we have two coordinates and to find the linear relationship we must find out the slope/gradient(m) of the linear function by the formula of slope:

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{160-70}{8-2} \\\\m=\frac{90}{6} \\\\m=15$

so we plug in one of the coordinates and our slope in the point-slope formula :

$y-y_1=m(x-x_1)$

where,

$(x_1,y_1)\ represent\ the\ coordinate\ (2,70)$

so plugging in the coordinate and the value of m we get:

$y-y_1=m(x-x_1)\\y-70=15(x-2)\\y-70=15x-30\\y=15x-30+70\\y=15x+40$

so our the answer is the last option

Y(n)=15n+40

here x corresponds to n and y corresponds to Y(n)