Question

for this item, drag the answers into the appropriate boxes.
a colony of termites eats a wooden board. the scatter plot shows the length of the board, y, in inches, based on the number of hours, x, after the termites begin eating the board, where
x < 0.
complete the sentence.
the equation best models the data, and the wooden board is approximately inches in length 4 hours after the termites begin eating the board.

Explanation:

Step1: Find two points on the line of best fit

Let's take two points \((x_1,y_1)=(10, 10)\) and \((x_2,y_2)=(30,30)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values: \(m=\frac{30 - 10}{30 - 10}= 1.5\)

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using \(m = 1.5\) and \((x_1,y_1)=(10,10)\), we have \(y-10 = 1.5(x - 10)\)

Step4: Simplify the equation

$$
LATEXBLOCK0
$$

Step5: Find the value of \(y\) when \(x = 4\)

Substitute \(x = 4\) into \(y = 1.5x-5\), \(y=1.5\times4-5=6 - 5=1\)

Answer:

The equation \(y = 1.5x-5\) best models the data. The wooden board is approximately \(1\) inches in length \(4\) hours after the termites begin eating the board.