Question

28,627 Learners found this answer helpful

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 first yellow point is at \((0, 30)\) (when \(x = 0\), \(y = 30\)) and the second yellow point is at \((90, 60)\) (when \(x = 90\), \(y = 60\)).

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

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((x_1,y_1)=(0,30)\) and \((x_2,y_2)=(90,60)\):

$$ m=\frac{60 - 30}{90 - 0}=\frac{30}{90}=\frac{1}{3} $$

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

The slope - intercept form of a line is \(y = mx + b\), where \(b\) is the y - intercept. When \(x = 0\), \(y = 30\) (from the point \((0,30)\)), so \(b = 30\).

Step4: Write the equation

Substituting \(m=\frac{1}{3}\) and \(b = 30\) into the slope - intercept form \(y=mx + b\), we get:

$$ y=\frac{1}{3}x + 30 $$

Answer:

\(y=\frac{1}{3}x + 30\)