Question

which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of $\frac{1}{3}$?$\bigcirc y + 2 =\frac{1}{3}(x + 3)$$\bigcirc y - 2 = \frac{1}{3}(x - 3)$$\bigcirc y + 3 = \frac{1}{3}(x + 2)$$\bigcirc y - 3 = \frac{1}{3}(x - 2)$

Explanation:

Step1: Recall point-slope formula

The point-slope form of a line is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

Step2: Substitute given values

Here, $(x_1, y_1) = (3, 2)$ and $m = \frac{1}{3}$. Substitute into the formula:
$y - 2 = \frac{1}{3}(x - 3)$

Step3: Match with options

Compare the derived equation to the provided choices.

Answer:

B. $y - 2 = \frac{1}{3}(x - 3)$