Question

what is the equation of the trend line in the scatter plot? use the two orange 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 orange points

From the scatter plot, the two orange points are \((2, 9)\) and \((6, 3)\).

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

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(2,9)\) and \((x_2,y_2)=(6,3)\). Then \(m=\frac{3 - 9}{6 - 2}=\frac{-6}{4}=-\frac{3}{2}\).

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

Use the slope-intercept form \(y = mx + b\) and one of the points, say \((2, 9)\). Substitute \(x = 2\), \(y = 9\), and \(m=-\frac{3}{2}\) into the equation:

$$ 9=-\frac{3}{2}(2)+b $$

Simplify the right side: \(-\frac{3}{2}(2)=-3\), so \(9=-3 + b\). Add 3 to both sides: \(b = 12\).

Step4: Write the equation

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

Answer:

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