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Hi,

a) Lines are perpendicular if their slopes are negative reciprocals of each other, like 3/5 and -5/3. Except for horizontal and vertical lines that are perpendicular the slopes of other perpendicular lines will always multiply together and equal -1. S 3/5 * -5/3 = -15/15 = -1 so these are perpendicular slopes.

b) Lines are intersecting anytime there slopes are different from each other. A special case of intersecting lines are the perpendicular lines we already discussed.

c) Lines are parallel if they have the same slope.

Slopes are generally found by putting equations into slope-intercept form, y = mx + b, where "m" is the slope of the line.

I hope that helps!! :-)

Perpendicular lines have the conjugate of the other line.

Example: a line with the slope of 8/3x would be perpendicular with a line of -3/8x.

Parallel lines are any lines with the same slope.

Example: a line with the slope 1/2x would be parallel with a line with the slope 1/2x.

Intersecting lines... I'm not sure about. If they aren't parallel, they ought to cross, but that's usually only for straight lines. Parabolas and other such lines are different and I haven't gotten to that point in the curriculum yet.

Put both lines in point-slope form, y = mx + b. m is the slope and b is the y-intercept.

If the slopes are negative reciprocals, they're perpendicular.

y = 1/2 x + 1 and y = -2 x - 3 are perpendicular

y = 2/3 x + 7 and y = -3/2 x + 4 are perpendicular

y = 2/3 x + 7 and y = 3/2 x + 4 are NOT perpendicular.

If the slope is the same, they're parallel.

y = 1/2 x + 1 and y = 1/2 x + 3 are parallel.

If the slopes ARE NOT the same, the lines are not parallel, and they intersect by definition.

perpendicular lines have opposite reciprocals for slopes (i.e. 2 and -1/2)

intersecting lines have shared coordinate where they cross (does that one make sense?)

parallel lines have the same slope but different y-intercepts

Hope that helps

for perpindicular, the slope is the opposite reciprocal (so instead of 1/2 it's -2)

for intersecting, at some point they have the same point (so they meet. not much more than that)

for parallel, the slopes are the same (like 1/2 and 1/2)

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They have different slopes so they are intersecting. That's all since to be perpendicular they need to have opposite reciprocal slopes, but these just have opposite slopes. (the slope in y = mx + b is m)

perpendicular- cross to form 4 right angles

intersecting- cross at any point

parallel- will never cross at any point