Find an equation for the line parallel to 4y+8x=12 and goes through the point (-8,4)

Question

Find an equation for the line parallel to 4y+8x=12 and goes through the point (-8,4)

Answer 1

For problems like this I like to put the equations into slope-intercept form ( y = mx + b). So, we are going to solve the equation for y:

4y + 8x = 12

4y = -8x + 12

y = -2x + 3

So, the slope of the original line give is -2. A line parallel to this will have a slope that is the opposite reciprocal. Opposite means the opposite sign (i.e. positive turns to negative and vice versa) and the reciprocal is flipping the number (i.e. 3 becomes 1/3). So since we have -2, it's going to be the opposite sign (positive 2) and it's going to be flipped. (1/2) This is what we have so far for our new line:

y = 1/2x + b

We need to find our b which is the y-intercept. To do this, we are going to plug the point in that they gave us so x and y and then solve for b:

4 = (1/2) * -8 + b

4 = -4 + b

+4 +4

8 = b

Now we can plug in our b into our equation:

y = 1/2x + 8