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: Find the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,30)\) and \((x_2,y_2)=(70,90)\).
\(m=\frac{90 - 30}{70 - 0}=\frac{60}{70}=\frac{6}{7}\)

Step2: Use the slope - intercept form \(y = mx + b\)

The slope - intercept form is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
We know that when \(x = 0\), \(y=30\), so \(b = 30\)
Substitute \(m=\frac{6}{7}\) and \(b = 30\) into \(y=mx + b\)
\(y=\frac{6}{7}x+30\)

Answer:

\(y=\frac{6}{7}x + 30\)