Question

which equation represents a line that passes through (5, 1) and has a slope of $\frac{1}{2}$?
$\bigcirc$ $y - 5 = \frac{1}{2}(x - 1)$
$\bigcirc$ $y - \frac{1}{2} = 5(x - 1)$
$\bigcirc$ $y - 1 = \frac{1}{2}(x - 5)$
$\bigcirc$ $y - 1 = 5\left(x - \frac{1}{2}\
ight)$

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, $(x_1, y_1) = (5, 1)$ and $m = \frac{1}{2}$. Substitute into the formula:
$y - 1 = \frac{1}{2}(x - 5)$

Step3: Match with options

Compare the derived equation to the provided choices.

Answer:

$y - 1 = \frac{1}{2}(x - 5)$