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

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using points \((0,4)\) and \((8,10)\), we have \(m=\frac{10 - 4}{8 - 0}=\frac{6}{8}=\frac{3}{4}\).

Step2: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\). Since \(b = 4\) (the \(y\) - intercept when \(x = 0\)) and \(m=\frac{3}{4}\), the equation is \(y=\frac{3}{4}x+4\).

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

Substitute \(y = 13\) into the equation \(13=\frac{3}{4}x+4\).
First, subtract 4 from both sides: \(13 - 4=\frac{3}{4}x\), so \(9=\frac{3}{4}x\).
Then, multiply both sides by \(\frac{4}{3}\): \(x=9\times\frac{4}{3}=12\).

Answer:

\(x = 12\)