Question

12,576 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

The first yellow point is at \((0, 70)\) (when \(x = 0\), \(y = 70\)) and the second yellow point is at \((60, 30)\) (when \(x = 60\), \(y = 30\)).

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

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

$$ m=\frac{30 - 70}{60 - 0}=\frac{-40}{60}=-\frac{2}{3} $$

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

The slope - intercept form of a line is \(y = mx + b\). The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0,70)\), when \(x = 0\), \(y = 70\), so \(b = 70\).

Step4: Write the equation in slope - intercept form

Substitute \(m=-\frac{2}{3}\) and \(b = 70\) into \(y=mx + b\). We get:

$$ y=-\frac{2}{3}x + 70 $$

Answer:

\(y = -\frac{2}{3}x + 70\)