# Thread: If lines are perpindicular or parallel

1. ## If lines are perpindicular or parallel

hi i have exams in the morning and i need help with a question

Decide whether Line 1 and LIne 2 are parallel, perpindicular, or neither

Line 1 passes through (-9,-8) and (-4,-4)
Line 2 passes through (-7,-2) and (-11,3)

2. Find the slopes of the two lines using the formula:
$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

where $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are your two points for a line.

Now what relationship between the two slopes will determine whether or not they're parallel or perpendicular?

3. it's all in the slopes. Use the points that have been supplied to calculate the slopes of the lines, then compare the slopes:

(1)If the slopes are the same number ( $m_1=m_2$), then the lines are parallel, or possibly concurrent.

(2)If the product of the slopes is -1 ( $m_1m_2=-1$), then the lines are perpendicular.

(3)If neither of the above two relationships are true, the the lines are neither parallel nor perpendicular.

4. teuthid can't you also graph the slopes?

If you're working some special, hand-crafted problems from a high-school algebra book, you might get lucky and be able to eye-ball it. However, in general, graphing is not a reliable way to determine if lines are parallel or perpendicular. If you graph two lines that meet at an angle of 89.993° (Perpendicular lines must intersect at 90° angles), then unless you can distinguish a difference of 0.007° degrees visually, you will wrongly guess that the lines were perpendicular. Similar problems arise when trying to determine if two lines are parallel (how do we know that the two lines don't intersect somewhere off the graph--perhaps a couple of miles away?).
Another problem would be drawing a graph where the scale of the axis is different. Two lines that are in fact perpendicular would not look it on a graph where the y-scale was 2 and the x-scale 1.
Basically, what I'm trying to say is that the only reliable way to determine if two lines are parallel or perpendicular is to test them algebraically as we've done here.

6. well it dosent look like hes doing some high school work i mean like the question looks like its from a middle school test, so i guess the teacher would take a simple answer if it was parallel/perpendicular/ neither. I kind of get what you are saying [im only in 8th grade]. I just learned this about 3 months ago so i remember graphing slopes and stuff.

7. I suppose if they've just introduced the topic then they might be nice about it and not give you examples with deceptive graphs. Just remember my warning in years to come as you study more advanced mathematics. From a mathematician's perspective, graphs are only useful insomuch as they show things that might be true. However, because they are always imperfect representations of whatever math thing that they're modeling, we can never trust them completely and must rely on logical arguments to know stuff for certain.

8. Originally Posted by cakes2010
hi i have exams in the morning and i need help with a question

Decide whether Line 1 and LIne 2 are parallel, perpindicular, or neither

Line 1 passes through (-9,-8) and (-4,-4)
Line 2 passes through (-7,-2) and (-11,3)

cakes,

We need to do 3 things in this question. I think it will be easier if you see the numbers and equations in action:

Step 1, calculate the slope/line equation of Line 1 that passes through the 2 points.

Go here: Slope, Line Equation, Distance, and Midpoint

Enter your first set of points and press calculate. Your Line Equation 1 is 4/5x - 4/5. Read the math work and see how we calculate the first 2 items. Ignore the distance and midpoint.

Now, enter your 2nd set of points and press calculate. Your Line Equation 2 is -5/4x - 43/4.

Step 3, determine if the 2 lines are parallel, perpendicular, or neither. In order to be parallel, the 2 lines must have equal slopes. They don't. If they are perpendicular, the product of their 2 slopes must be -1. Taking (4/5)(-5/4), we get -1. This means the 2 lines are perpendicular. Had their product not been -1 and the 2 slopes not equal to each other, we would have had the 3rd answer of "neither". That sums it up for your problem.

In the future, if you ever have 2 lines that intersect, and you want to see the intersection point, enter your line equations here:

Determine if 2 lines are parallel-perpendicular-intersecting

Use decimal form for fractions. This will show you how to setup your equations to determine an intersection point if it exists like it does here.