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: Rewrite given line in slope - intercept form

Rewrite $x + 2y=4$ as $y=-\frac{1}{2}x + 2$. The slope of this line is $m =-\frac{1}{2}$. Since parallel lines have the same slope, the line we want to find also has a slope of $m =-\frac{1}{2}$.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Substitute $x_1=-4$, $y_1 = - 1$ and $m=-\frac{1}{2}$ into it. We get $y-(-1)=-\frac{1}{2}(x - (-4))$.

Step3: Simplify the equation

$y + 1=-\frac{1}{2}(x + 4)$. Expand the right - hand side: $y+1=-\frac{1}{2}x-2$. Then subtract 1 from both sides to get $y=-\frac{1}{2}x-3$. Multiply through by 2 to get the general form: $x + 2y=-6$.

Answer:

$x + 2y=-6$