Question

question
what is the equation of the line that passes through the point $(6, 1)$ and has a slope of $-\frac{1}{2}$?

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)=(6,1)$ and $m=-\frac{1}{2}$.
$y - 1 = -\frac{1}{2}(x - 6)$

Step2: Simplify to slope-intercept form

Distribute the slope and isolate $y$.
$y - 1 = -\frac{1}{2}x + 3$
$y = -\frac{1}{2}x + 3 + 1$
$y = -\frac{1}{2}x + 4$

Answer:

$y = -\frac{1}{2}x + 4$ (or in standard form: $x + 2y = 8$)