Answer:
Option A is correct.
\(y-16=8(x-2)\) is the equation represent the point slope form gives the plant's height at any time.
Step-by-step explanation:
Point slope intercept form: For any two points \((x_1, y_1)\) and \((x_2, y_2)\) then,
the general form
\(y-y_1=m(x-x_1)\) for linear equations; where m is the slope given by:
\(m =\frac{y_2-y_1}{x_2-x_1}\)
Consider any two points from the table;
let A= (2 , 16) and B =(4, 32)
First calculate the slope of the line AB:
\(m =\frac{y_2-y_1}{x_2-x_1}=\frac{32-16}{4-2}=\frac{16}{2}\) = 8
Therefore, slope of the line m = 8
Then,
the equation of line is:
\(y-y_1=m(x-x_1)\)
Substitute the value of m=8 and (2, 16) above we get;
\(y-16=8(x-2)\)
Therefore, the equation in point slope form which gives the plant's height at any time is; \(y-16=8(x-2)\) , where x is the time(months) and y is the plant height (cm)
