SOLUTION: Are the following lines parallel, perpendicular, or neither? L1 through (�4, �7) and (1, 3) L2 through (2, 6) and (4, 10)

Question 127128: Are the following lines parallel, perpendicular, or neither?
L1 through (�4, �7) and (1, 3)
L2 through (2, 6) and (4, 10)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First find the slope through (-4, -7) and (1, 3)

-------------------------------------------

Let's denote the first point (-4,-7) as

. In other words,

and

Now let's denote the second point (1,3) as

. In other words,

and

-------------------------

Start with the slope formula

Plug in ,,,

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope of the line through the points (-4,-7) and (1,3) is

-------------------------------------------

Now let's find the slope through (2, 6) and (4, 10)

Let's denote the first point (2,6) as

. In other words,

and

Now let's denote the second point (4,10) as

. In other words,

and

-------------------------

Start with the slope formula

Plug in ,,,

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope of the line through the points (2,6) and (4,10) is

--------------------------------

Since the slope through the two pairs of points is , this means that the two lines are parallel
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