Question

what is the equation of the trend line in the scatter plot? use the two blue 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 - blue points

Let the two blue points be $(x_1,y_1)=(4,0)$ and $(x_2,y_2)=(8,6)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute the values: $m=\frac{6 - 0}{8 - 4}=\frac{6}{4}=\frac{3}{2}$.

Step3: Use the point - slope form to find the y - intercept $b$

The slope - intercept form is $y=mx + b$. Use the point $(4,0)$ and $m = \frac{3}{2}$. Substitute into the equation: $0=\frac{3}{2}\times4 + b$. Simplify the right - hand side: $\frac{3}{2}\times4=6$, so $0 = 6 + b$. Solve for $b$: $b=-6$.

Step4: Write the equation in slope - intercept form

The equation of the line is $y=\frac{3}{2}x-6$.

Answer:

$y=\frac{3}{2}x - 6$