Question

given the scatter plot below, write the equation for the line of best fit in slope - intercept form.

Explanation:

Step1: Identify two points on the line

Looking at the line of best fit, we can identify two clear points. Let's take \((0, 6)\) (the y - intercept) and \((2, 10)\).

Step2: Calculate the slope (\(m\))

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((x_1,y_1)=(0,6)\) and \((x_2,y_2)=(2,10)\), we have \(m=\frac{10 - 6}{2 - 0}=\frac{4}{2} = 2\).

Step3: Determine the y - intercept (\(b\))

The slope - intercept form of a line is \(y=mx + b\), where \(b\) is the y - intercept. From the point \((0,6)\), when \(x = 0\), \(y=b\). So \(b = 6\).

Step4: Write the equation

Substitute \(m = 2\) and \(b = 6\) into the slope - intercept form \(y=mx + b\). We get \(y = 2x+6\).

Answer:

\(y = 2x + 6\)