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 - point coordinates

Let the first yellow point be $(x_1,y_1)=(10,40)$ and the second yellow point be $(x_2,y_2)=(60,60)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute the values: $m=\frac{60 - 40}{60 - 10}=\frac{20}{50}=\frac{2}{5}$.

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

The slope - intercept form is $y=mx + b$. Use the point $(10,40)$ and $m = \frac{2}{5}$. Substitute into the equation: $40=\frac{2}{5}\times10 + b$.
Simplify the right - hand side: $\frac{2}{5}\times10=4$, so $40 = 4 + b$.
Solve for $b$: $b=40 - 4=36$.

Step4: Write the equation of the line

The equation of the line in slope - intercept form is $y=\frac{2}{5}x+36$.

Answer:

$y=\frac{2}{5}x + 36$