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 are (0, 2) and (6, 6).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(6,6)$ into the formula: $m=\frac{6 - 2}{6-0}=\frac{4}{6}=\frac{2}{3}$.

Step3: Find the y - intercept $b$

The slope - intercept form is $y = mx + b$. Using the point $(0,2)$ (where $x = 0$ and $y = 2$) and $m=\frac{2}{3}$, we substitute into the equation. When $x = 0$, $y=b$. So $b = 2$.

Step4: Write the equation of the line

Substitute $m=\frac{2}{3}$ and $b = 2$ into $y=mx + b$. The equation is $y=\frac{2}{3}x + 2$.

Answer:

$y=\frac{2}{3}x + 2$