Question

practice comparing linear functions of real - world scenarios. plant a: in science, students are observing the growth of two plants. plant a receives sunlight and plant b does not. the graph and table show the data for this scenario. what is the initial height of plant b? inches plant b: weeks height (in) 2 7.3 3 8.7 4 10.1

Explanation:

Step1: Find the slope of Plant B's growth

The slope $m$ of a linear - function is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(2,7.3)$ and $(3,8.7)$ from the table of Plant B, we have $m=\frac{8.7 - 7.3}{3 - 2}=\frac{1.4}{1}=1.4$.

Step2: Use the point - slope form of a line

The point - slope form of a line is $y - y_1=m(x - x_1)$. Let's use the point $(2,7.3)$ and $m = 1.4$. The equation of the line is $y-7.3 = 1.4(x - 2)$.

Step3: Find the initial height (when $x = 0$)

Substitute $x = 0$ into the equation $y-7.3=1.4(x - 2)$.
\[

$$\begin{align*} y-7.3&=1.4(0 - 2)\\ y-7.3&=1.4\times(-2)\\ y-7.3&=-2.8\\ y&=7.3-2.8\\ y&=3.5 \end{align*}$$

\]
So the initial height of Plant B is 3.5 inches.

Answer:

3.5