Question

What is the equation of the line AB, if it passes through (-4,0), and is parallel to the line

Answer 1

Rewriting the equation of the given line in slope-intercept form,

$-x-4y=1\\\\-4y=x+1\\\\4y=-x-1\\\\y=-\frac{1}{4}x-\frac{1}{4}$

From this, we know the slope of the given line is -1/4.

Since parallel lines have the same slope, we know the line whose equation we want to find has a slope of -1/4.

Substituting into point-slope form,

$y=-\frac{1}{4}(x+4)\\\\\boxed{y=-\frac{1}{4}x-1}$