Tell whether the lines through the given points are parallel,perpendicular or neither

Question

Line 1:(-3,1), (-7,-2)

Line 2;(2,-1),(8,4)

Answer 1

Hi Kim

 

First we need to find the slope of the line between line 1.

 

We use the formula:

 

y₂ - y₁ / x₂ - x₁

 

-2 - 1 / -7 - (-3)  ---> this gives us -3 / -4 or simply 3/4. So our slope for line 1 is 3/4.

 

Now using the formula, (y - y₁) = m (x - x₁) we find the line.

 

(y - 1) = 3/4 (x - (-3)) ---> (y - 1) = 3/4x + 9/4.

 

Now we add one to each side to get y = 3/4x + 13/4.

 

Now for line 2, we use the same process and formulas.

 

Find the slope of line 2.

 

4 - (-1) / 8 - 2 gives us 5/6. Our slope for line 2 is 5/6.

 

(y - (-1)) = 5/6 (x - 2).

 

(y + 1) = 5/6x - 5/3 ---> now subtract one from both sides to get...

 

y = 5/6x - 8/3.

 

Since the two lines do not have the same slope or the negative reciprocal of one slope being the other, the two lines through the given points are neither parallel nor are they perpendicular.

 

NEITHER

Answer 2

Kim, remember that parallel lines have the same slope. Perpendicular lines have the opposite reciprocal slope, like 3/4 and -4/3.

 

Do you remember how to find the slope?  I think you can do this!