Question

what is the equation of the trend line in the scatter plot? use the two blue points to write the equation in slope - intercept form. write any coefficients as integers, proper fractions, or improper fractions in simplest form.

Explanation:

Step1: Identify the two blue points

From the graph, the two blue points are \((4, 6)\) and \((8, 0)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 4\), \(y_1 = 6\), \(x_2 = 8\), \(y_2 = 0\):
\(m=\frac{0 - 6}{8 - 4}=\frac{-6}{4}=-\frac{3}{2}\)

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

Use the slope-intercept form \(y = mx + b\) and one of the points, say \((8, 0)\). Substitute \(m = -\frac{3}{2}\), \(x = 8\), \(y = 0\):
\(0=-\frac{3}{2}(8)+b\)
\(0=-12 + b\)
\(b = 12\)

Step4: Write the equation

Substitute \(m = -\frac{3}{2}\) and \(b = 12\) into \(y = mx + b\):
\(y=-\frac{3}{2}x + 12\)

Answer:

\(y = -\frac{3}{2}x + 12\)