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: Use point - slope form to find the equation

The point - slope form is \(y - y_1=m(x - x_1)\). Using the point \((10, 0)\) and \(m=\frac{3}{2}\):

$$ y - 0=\frac{3}{2}(x - 10) $$

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

$$ y=\frac{3}{2}x-\frac{3}{2}\times10=\frac{3}{2}x - 15 $$

We can also check with the other point \((70,90)\). Substitute \(x = 70\) into \(y=\frac{3}{2}x-15\):

$$ y=\frac{3}{2}\times70-15 = 105 - 15=90 $$

, which matches the \(y\) - coordinate of the second point.

Answer:

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