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 $y = 20$?

Explanation:

Step1: Find the slope of the line

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0,4)\) and \((5,8)\):
\(m=\frac{8 - 4}{5 - 0}=\frac{4}{5}=0.8\)

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 \(m=0.8\), the equation is \(y=0.8x + 4\)

Step3: Solve for \(x\) when \(y = 20\)

Substitute \(y = 20\) into the equation \(20=0.8x + 4\)
Subtract \(4\) from both sides: \(20−4=0.8x\), so \(16 = 0.8x\)
Divide both sides by \(0.8\): \(x=\frac{16}{0.8}=20\)

Answer:

\(20\)