Question

what is the equation of the trend line in the scatter plot? use the two orange 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 - point coordinates

The two orange points are approximately $(4,2)$ and $(6,9)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(4,2)$ and $(x_2,y_2)=(6,9)$ into the formula: $m=\frac{9 - 2}{6 - 4}=\frac{7}{2}$.

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

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(4,2)$ and $m = \frac{7}{2}$, we have $y-2=\frac{7}{2}(x - 4)$. Expand the right - hand side: $y-2=\frac{7}{2}x-14$. Add 2 to both sides to get the slope - intercept form $y=mx + b$: $y=\frac{7}{2}x-12$.

Answer:

$y=\frac{7}{2}x - 12$