Final answer:
To find the equation for parallel lines, use the same slope. For perpendicular lines, find the negative reciprocal of the slope.
Step-by-step explanation:
To find the equation for parallel lines, you need the slope of the given line. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since parallel lines have the same slope, the equation for a line parallel to the given line will have the same slope.
To find the equation for perpendicular lines, you need to find the negative reciprocal of the slope of the given line. The negative reciprocal is obtained by flipping the fraction and changing the sign. The equation for a line perpendicular to the given line will have the negative reciprocal slope.
For example, if the equation of the given line is y = 2x + 3, a line parallel to it will have the same slope of 2, resulting in an equation of y = 2x + b. A line perpendicular to it will have a slope of -1/2 (the negative reciprocal of 2), resulting in an equation of y = (-1/2)x + b.