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: Find the slope \(m\)

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(4,4)\) and \((x_2,y_2)=(8,9)\). Then \(m=\frac{9 - 4}{8 - 4}=\frac{5}{4}\).

Step2: Find the \(y\) - intercept \(b\)

Use the slope - intercept form \(y = mx + b\) and substitute \(m=\frac{5}{4}\), \(x = 4\), \(y = 4\).
\(4=\frac{5}{4}\times4 + b\)
\(4 = 5 + b\)
\(b=-1\)

Step3: Write the equation

Substitute \(m=\frac{5}{4}\) and \(b = - 1\) into \(y=mx + b\). The equation is \(y=\frac{5}{4}x-1\).

Answer:

\(y=\frac{5}{4}x - 1\)