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: Identify the two yellow points

From the scatter plot, the two yellow points are \((10, 0)\) and \((70, 90)\).

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

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 10\), \(y_1 = 0\), \(x_2 = 70\), \(y_2 = 90\):

$$ m=\frac{90 - 0}{70 - 10}=\frac{90}{60}=\frac{3}{2} $$

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

Using the slope - intercept form \(y = mx + b\) and the point \((10, 0)\) (we can also use \((70,90)\)). Substitute \(x = 10\), \(y = 0\), and \(m=\frac{3}{2}\) into \(y=mx + b\):

$$ 0=\frac{3}{2}(10)+b $$

$$ 0 = 15 + b $$

Subtract 15 from both sides: \(b=- 15\)

Step4: Write the equation

The slope - intercept form is \(y=mx + b\). Substituting \(m = \frac{3}{2}\) and \(b=-15\):

$$ y=\frac{3}{2}x-15 $$

Answer:

\(y=\frac{3}{2}x - 15\)