Parallel lines have the same slope. Perpendicular lines have slopes that are the negative reciprocals of each other.
So, to do this problem, you need to compare the slopes of the two lines. Obviously, to compare the slopes, you need to figure out what the slopes are for each line. The easiest way to do this is to rearrange the equations by putting them into the y = mx + b format. The slope (m) will be the coefficient in front of the x.
6 + 8x = 4y is almost in the right format, just divide both sides by 4
6/4 + (8/4)x = y or y = 2x + 3/2 so the slope is 2.
For 4x + 8y = 5, move the 4x to the other side by subtracting 4x from both sides of the equation
8y = -4x + 5 Now, divide both sides by 8
y = -(4/8)x + 5 or y = -(1/2)x + 5 so the slope is -1/2
One line has a slope of 2 and the other line has a slope of -1/2. Those are negative reciprocals of each other (2 is the same as 2/1 and if I flip it over to get the reciprocal, I get 1/2 then if I make that a negative, I get -1/2). So the lines are perpendicular.
