Question

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

-x - 4y = 1?

Answer 1

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

`-x-4y=1\\\\-4y=x+1\\\\4y=-x-1\\\\y=-(1)/(4)x-(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=-(1)/(4)(x+4)\\\\\boxed{y=-(1)/(4)x-1}`