Question

find the equation of the line parallel to $2x - 4y = -2$ and passes through the point $(-1, -2)$. select one: \\(\bigcirc\\) a. $y = \dfrac{1}{2}x - \dfrac{3}{2}$ \\(\bigcirc\\) b. $y = \dfrac{1}{2}x - 1$ \\(\bigcirc\\) c. $y = -\dfrac{1}{2}x - \dfrac{5}{2}$ \\(\bigcirc\\) d. $y = \dfrac{1}{2}x + \dfrac{5}{2}$

Explanation:

Step1: Convert to slope-intercept form

Rewrite $2x - 4y = -2$ to $y=mx+b$:
$-4y = -2x -2$
$y = \frac{-2x -2}{-4} = \frac{1}{2}x + \frac{1}{2}$
Slope $m = \frac{1}{2}$

Step2: Use point-slope formula

Parallel lines have equal slopes. Use point $(-1,-2)$:
$y - y_1 = m(x - x_1)$
$y - (-2) = \frac{1}{2}(x - (-1))$

Step3: Simplify to slope-intercept

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

Answer:

A. $y = \frac{1}{2}x - \frac{3}{2}$