Question

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

Explanation:

Step1: Identify the initial height concept

The initial height of a plant in a linear relationship (like the graph here) is the height when time \(x = 0\).

Step2: Use the slope - intercept form \(y=mx + b\)

The slope - intercept form of a line is \(y=mx + b\), where \(b\) is the \(y\) - intercept (initial value).
We can find the slope \(m\) using two points \((x_1,y_1)=(1,4.8)\) and \((x_2,y_2)=(2,6.6)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

$$m=\frac{6.6 - 4.8}{2 - 1}=\frac{1.8}{1}=1.8$$

Now use the point - slope form \(y - y_1=m(x - x_1)\) with the point \((x_1,y_1)=(1,4.8)\) and \(m = 1.8\).

$$y-4.8=1.8(x - 1)$$

$$y-4.8=1.8x-1.8$$

$$y=1.8x + 3$$

When \(x = 0\), \(y=3\) (since in \(y=mx + b\), when \(x = 0\), \(y=b\)).

Answer:

\(3\)