Question

a line of best fit was drawn to the plotted points in a data set below. based on the line of best fit, for what x-value does y = 13?

Explanation:

Step1: Find the slope of the line

We have two points on the line: \((0, 4)\) and \((4, 7)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{7 - 4}{4 - 0}=\frac{3}{4}\).

Step2: Write the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((0,4)\) (where \(x_1 = 0\) and \(y_1 = 4\)) and \(m=\frac{3}{4}\), the equation of the line is \(y-4=\frac{3}{4}(x - 0)\), which simplifies to \(y=\frac{3}{4}x + 4\).

Step3: Solve for \(x\) when \(y = 13\)

Substitute \(y = 13\) into the equation \(y=\frac{3}{4}x+4\):
\[

$$\begin{align*} 13&=\frac{3}{4}x + 4\\ 13-4&=\frac{3}{4}x\\ 9&=\frac{3}{4}x\\ x&=9\times\frac{4}{3}\\ x& = 12 \end{align*}$$

\]

Answer:

\(12\)