Question

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

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

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 3\), \(y_1 = 3\), \(x_2 = 6\), \(y_2 = 9\) into the formula:
\(m=\frac{9 - 3}{6 - 3}=\frac{6}{3}=2\)

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

Use the slope - intercept form \(y = mx + b\) and one of the points, say \((3, 3)\). Substitute \(m = 2\), \(x = 3\), and \(y = 3\) into the equation:
\(3=2\times3 + b\)
\(3 = 6 + b\)
Subtract 6 from both sides: \(b=3 - 6=- 3\)

Step4: Write the equation

Using the slope - intercept form \(y=mx + b\) with \(m = 2\) and \(b=-3\), the equation is \(y = 2x-3\)

Answer:

\(y = 2x - 3\)