I’m confuse. Please help me.

Question

Are the graphs of the two lines parallel, perpendicular, or neither?

The line containing the two points (3,5) and (-2,-1)

The line containing the two points (-2,3) and (4,-2)

Answer 1

Two lines are parallel if their slopes are the same.

Two lines are perpendicular if their slopes are negative reciprocals of each other.

The negative reciprocal of any number x is -(1/x).

To find the slope of a line, look at the two points that it contains.

Let's call these points (x₁, y₁) and (x₂, y₂).

The slope can be found with the following equation: (y₂-y₁) / (x₂-x₁).

So for your first line, x₁ = 3, y₁ = 5, x₂ = -2, and y₂ = -1.

For your 1st line, ( (-1) - (5) ) / ( (-2) - (3) ) = (-6) / (-5) = 6/5. So the slope is 6/5.

For your 2nd line, ( (-2) - (3) ) / ( (4) - (-2) ) = (-5) / (6) = -5/6. So the slope is -5/6.

The negative reciprocal of 6/5 is -(1/(6/5)) = -5/6.

Since 6/5 and -5/6 are negative reciprocals of each other, the two lines are perpendicular.

Answer 2

You are confused because you don't know how to tell whether two lines are parallel or perpendicular or neither.

REMEMBER: Two lines are PARALLEL if they have the SAME SLOPE.

REMEMBER: Two lines are PERPENDICULAR if their SLOPES are NEGATIVE RECIPROCALS of each other, like –2 and 1/2.

To find the slope of a line defined by two points, find the difference of the two y-coordinates by subtracting; put that number in the numerator. Find the difference of the two corresponding x-coordinates of the two points by subtracting; put that number in the denominator. Reduce the fraction if possible. That is the SLOPE of the line defined by the two points.

For example, for the line defined by (3,5) and (–2,–1):

5 – (–1) 5 + 1 6

________ = ________ = _____ SLOPE FOR LINE 1

3 – (–2) 3 + 2 5

Figure out the slope for the second line. Compare the two slopes, using the information that I asked you to remember, and then you can answer the question you were asked.