Question

write the equation of the line parallel to the given line and passing through the given point.
$y = -dfrac{1}{2}x + 4$, $(6, 2)$
answer

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For the given line $y=-\frac{1}{2}x+4$, the slope $m=-\frac{1}{2}$.

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $m=-\frac{1}{2}$, $x_1=6$, $y_1=2$.
$y-2=-\frac{1}{2}(x-6)$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y-2=-\frac{1}{2}x+3$
$y=-\frac{1}{2}x+3+2$
$y=-\frac{1}{2}x+5$

Answer:

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