# How do you write an equation of a line for Anne who wants to track the growth of the rose and finds that in the third week, the rose is 10 inches tall and in the eleventh week the rose is 14 inches tall.?

Nov 14, 2014

Let $y$ be the height of the rose, and let $x$ be time in weeks.

Since the rose is 10 inches tall in the third week, we write

$\left({x}_{1} , {y}_{1}\right) = \left(3 , 10\right)$

Since the rose is 14 inches tall in the eleventh week, we write

$\left({x}_{2} , {y}_{2}\right) = \left(11 , 14\right)$

By Slope Formula,

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{14 - 10}{11 - 3} = \frac{4}{8} = \frac{1}{2}$

By Point-Slope Form $y - {y}_{1} = m \left(x - {x}_{1}\right)$, we have the equation

$y - 10 = \frac{1}{2} \left(x - 3\right)$.

I hope that this was helpful.