Question

what is an equation of the line that passes through the point (-4, -1) and is parallel to the line x + 2y = 4?

Explanation:

Step1: Convert to slope-intercept form

Rearrange $x + 2y = 4$ to solve for $y$:
$2y = -x + 4$
$y = -\frac{1}{2}x + 2$

Step2: Identify parallel slope

Parallel lines have equal slopes, so $m = -\frac{1}{2}$.

Step3: Use point-slope formula

Substitute $m = -\frac{1}{2}$, $x_1=-4$, $y_1=-1$ into $y - y_1 = m(x - x_1)$:
$y - (-1) = -\frac{1}{2}(x - (-4))$

Step4: Simplify the equation

$y + 1 = -\frac{1}{2}(x + 4)$
$y + 1 = -\frac{1}{2}x - 2$
$y = -\frac{1}{2}x - 3$
Or in standard form: $x + 2y = -6$

Answer:

$y = -\frac{1}{2}x - 3$ (or $x + 2y = -6$)