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 two - point coordinates

The two yellow points seem to be approximately $(30,20)$ and $(60,70)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(30,20)$ and $(x_2,y_2)=(60,70)$ into it. So $m=\frac{70 - 20}{60 - 30}=\frac{50}{30}=\frac{5}{3}$.

Step3: Find the y - intercept $b$

Use the slope - intercept form $y=mx + b$ and substitute one of the points, say $(30,20)$ and $m = \frac{5}{3}$ into it. We get $20=\frac{5}{3}\times30 + b$. Simplify the right - hand side: $\frac{5}{3}\times30=50$, so $20 = 50 + b$. Solve for $b$: $b=20 - 50=-30$.

Step4: Write the equation

The equation of the line in slope - intercept form is $y=\frac{5}{3}x-30$.

Answer:

$y=\frac{5}{3}x - 30$