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Which is the best description for the lines m and k?
A)
parallel
B)
perpendicular
intersecting and parallel
D
intersecting but not perpendicular

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Explanation:

I've highlighted lines m and k in red (see diagram below). We'll ignore the other lines. On those red lines, I've added blue points with their coordinate locations.

Line m has point A = (-3, 5) and B = (-1, -3). Let's use the slope formula to find the slope through these points

m = (y2-y1)/(x2-x1)

m = (-3-5)/(-1-(-3))

m = (-3-5)/(-1+3)

m = -8/2

m = -4

The slope of line AB, aka line m, is -4.

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Line k has points C = (1, 5) and D = (3, -3) on it. We'll use the slope formula to get...

m = (y2-y1)/(x2-x1)

m = (-3-5)/(3-1)

m = -8/2

m = -4

The slope of line CD, aka line k, is -4

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Both lines m and k have the same slope of -4. Therefore, the two lines are parallel. Parallel lines always have the same slope, but different y intercepts. So these lines will never intersect one another.

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