what is an equation of the line that passes through the points (6,3) and (-6,1)?

Explanation:

Step1: Find the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(6,3)$ and $(x_2,y_2)=(-6,1)$. Then $m=\frac{1 - 3}{-6 - 6}=\frac{-2}{-12}=\frac{1}{6}$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(6,3)$ and $m = \frac{1}{6}$, we have $y - 3=\frac{1}{6}(x - 6)$.

Step3: Convert to slope - intercept form

Expand the right side: $y - 3=\frac{1}{6}x-1$. Add 3 to both sides to get $y=\frac{1}{6}x + 2$.

Answer:

$y=\frac{1}{6}x + 2$