Question

What is an equation of the line that passes through the point (-2, -6) and is

parallel to the line x + 2y = 8?

Answer 1

y = -1/2x - 7

Explanation:

First, let's get the line in slope-intercept form. This is of the form y = mx + b. This helpful because we will be able to tell what the slope is, which is important because the parallel line will have the same slope. To do this, we need to isolate y. Subtract x from both sides. This gives us
`2y = 8-x`. Now divide both sides by 2 to completely isolate y. This gives us
`y = (8-x)/2`, or
`y = -x/2 + 4`. From this we can tell that the slope is -1/2, because that is the coefficient of x.

This is the same slope we need for the parallel line! Let's put the line in slope-intercept form. We have our slope(-1/2), so we need to solve for b, which is the y-intercept. To do this, we will plug in the point on the graph to the equation for x an y. This gives us
`-6 = -1/2*-2 + b`, or
`-6 = 1 + b`. Subtracting 1 from both sides tells us that which tells us b = -7. This is the y-intercept! Now we can plug this and the slope into our equation to get our answer: y = -1/2x - 6

I hope this helps!