For this, there is two rules. The common slope-intercept form is y=ax + b. For parallel, b can change, but a, or the slope, can't change. But for perpendicular, the a should be -1/a, where the answer for times the original equation, or a, and the second equation, or -1/a, is -1. To prove these two rules, you can graph it using random numbers but follow these two rules. if you have any part that don't understand for this answer, feel free to ask in the "Ask for details" section.
