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.
$y = \frac{5}{4}x-\frac{15}{2}$

Explanation:

Step1: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(30,30)\) and \((x_2,y_2)=(70,80)\). Then \(m=\frac{80 - 30}{70 - 30}=\frac{50}{40}=\frac{5}{4}\).

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Substitute \(m = \frac{5}{4}\), \(x_1 = 30\), \(y_1 = 30\) into \(y - y_1=m(x - x_1)\). We get \(y-30=\frac{5}{4}(x - 30)\).

Step3: Simplify to slope - intercept form \(y=mx + b\)

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Answer:

\(y = \frac{5}{4}x-\frac{15}{2}\)