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: Find the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(30,10)\) and \((x_2,y_2)=(90,60)\).

$$m=\frac{60 - 10}{90 - 30}=\frac{50}{60}=\frac{5}{6}$$

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

Substitute \(m = \frac{5}{6}\), \(x_1 = 30\), \(y_1=10\) into \(y - y_1=m(x - x_1)\).

$$y-10=\frac{5}{6}(x - 30)$$

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

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Answer:

\(y=\frac{5}{6}x - 15\)