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

The two yellow points are $(20,0)$ and $(60,75)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(20,0)$ and $(x_2,y_2)=(60,75)$ into the formula: $m=\frac{75 - 0}{60 - 20}=\frac{75}{40}=\frac{15}{8}$.

Step3: Find the y - intercept $b$

The slope - intercept form is $y=mx + b$. We know $m=\frac{15}{8}$ and when $x = 20,y = 0$. Substitute into the equation: $0=\frac{15}{8}\times20 + b$. Solve for $b$: $0=\frac{15\times20}{8}+b$, $0=\frac{75}{2}+b$, $b=-\frac{75}{2}$.

Step4: Write the equation

The equation of the line in slope - intercept form is $y=\frac{15}{8}x-\frac{75}{2}$.

Answer:

$y=\frac{15}{8}x-\frac{75}{2}$