Question

Find the equation of the line through point (-4,1) and parallel to y= -1/2x-2.

Answer 1

Answer:

$y = -\frac{1}{2}x - 1$

Step-by-step explanation:

In order for two lines to be parallel they must have the same slope. In other words the m constant in the line equation needs to match

$y = mx + b$

This means for the equation we're trying to find, we already know m. It's just -1/2 since that's the slope of the line it needs to be parallel to.

Next, let's find the constant b. We know the slope, and we know it goes through points (-4, 1), so let's plug this into our equation

$y = -\frac{1}{2}x + b\\1 = - \frac{1}{2}\times{-4} + b\\1 = 2 + b\\b = -1$

Now that we have both constants, we know the equation of the line.

$y = -\frac{1}{2}x - 1$

To convince yourself this is correct, let's plot these two lines.