what is an equation of the line that passes through the points (3, 6) and (-3, 4)?

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(3,6)$ and $(x_2,y_2)=(-3,4)$. So $m=\frac{4 - 6}{-3 - 3}=\frac{-2}{-6}=\frac{1}{3}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Let's use the point $(3,6)$ and $m = \frac{1}{3}$. Then $y - 6=\frac{1}{3}(x - 3)$.

Step3: Simplify the equation

Expand the right - hand side: $y - 6=\frac{1}{3}x - 1$. Add 6 to both sides to get the slope - intercept form $y=\frac{1}{3}x+5$.

Answer:

$y=\frac{1}{3}x + 5$