First, put both equations in slope-intercept form, that is, y = mx + b. m is the slope of the line; if the slopes are the same, the lines are parallel. If you multiply the slopes and the answer is - 1, the lines are perpendicular. If I can be of further assistance, let me know.
The first step is to put both the equations in slope-intercept form (y = mx + b) form.
where m is the slope.
Now, you compare the slopes of the two equations
First, bring both the equations in slope-intercept form (y = mx + b) form.
Then compare slopes(m) of both equations. If the slopes are same then these lines are parallel to each other.
If, the slopes of line are negative reciprocal of each other then these lines are perpendicular to each other. And, if the lines have different slopes then the lines are intersecting lines.
For example y = 4x + 3, y = 4x - 5 (slope is 4 in both lines and they are same, that's why the lines are parallel)
y = 2x + 4, y = (-1/2)x + 3 (slope of first line is 2 and slope of second line is (-1/2). If you see slopes are negative reciprocal of each other, that's why the lines are perpendicular to each other)
y = 2x - 3, y = -3x + 4 (slope of first line is 2 and slope of second line is -3. In both equations of lines slope is different, that's why these lines are intersecting lines)
Good luck with your problem. If you still need some help we'll be glad to help you.