Parallel, Perpendicular, or Neither

• nycmathguy
Knowing what the problem is asking is the most important step in solving it.In summary, when solving a math problem, it is important to clearly state the homework statement and relevant equations in order to show a full understanding of the problem and the tools necessary to solve it.
nycmathguy
Homework Statement
Determine whether the lines are parallel,
perpendicular, or neither.
Relevant Equations
Linear Equations
Determine whether the lines are parallel,
perpendicular, or neither.

Line 1: y = (x/4) − 1

Line 2: y = 4x + 7

Looking at the slopes of the lines, I say neither. Is (1/4) the negative reciprocal of 4?
I say no.

You answer is correct but you provide half the justification. I guess you omit the other half (why they are not parallel) because it seems obvious to you.

Delta2 said:
You answer is correct but you provide half the justification. I guess you omit the other half (why they are not parallel) because it seems obvious to you.

The lines are not parallel because their slope is not the same.

Delta2
nycmathguy said:
Homework Statement:: Determine whether the lines are parallel,
perpendicular, or neither.
Relevant Equations:: Linear Equations

Determine whether the lines are parallel,
perpendicular, or neither.

Line 1: y = (x/4) − 1

Line 2: y = 4x + 7

Looking at the slopes of the lines, I say neither. Is (1/4) the negative reciprocal of 4?
I say no
.

nycmathguy said:
The lines are not parallel because their slope is not the same.
I think @Mark44 has given you this tip before, but the "Relevant Equations" is a place where you should explicitly list the equations or methods that can be used to solve the problem, not for a general statement like "Linear Equations".

In this case, while solving the problem you did list the relevant concepts / conditions for parallel and perpendicular lines. Those should have been listed in the Relevant Equations section at the start, and then you can apply those conditions to the problem (finding the slopes and using the Relevant Equations/Conditions) to solve the problem. Does that make sense?

berkeman said:
I think @Mark44 has given you this tip before, but the "Relevant Equations" is a place where you should explicitly list the equations or methods that can be used to solve the problem, not for a general statement like "Linear Equations".

In this case, while solving the problem you did list the relevant concepts / conditions for parallel and perpendicular lines. Those should have been listed in the Relevant Equations section at the start, and then you can apply those conditions to the problem (finding the slopes and using the Relevant Equations/Conditions) to solve the problem. Does that make sense?

Not really. Can you give me another example of RELEVANT EQUATIONS?

Say the problem is solve y = mx + b for b.

1. What is the HW Statement?
2. What should the Relevant Equations be?

nycmathguy said:
Say the problem is solve y = mx + b for b.

1. What is the HW Statement?
2. What should the Relevant Equations be?
The HW statement is what you listed, and to solve it you use simple algebraic manipulations, so you probably don't need to list those (distributivity, associativity, etc.).

In the problem for this thread, the Relevant Equations/Information would be something like:

Parallel Lines: Have the same slope
Perpendicular Lines: Have inverse slopes

nycmathguy said:
Say the problem is solve y = mx + b for b.

1. What is the HW Statement?
2. What should the Relevant Equations be?
Homework Statement: solve y = mx + b for b
For this trivial example, I'd be fine with leaving the Relevant Equations section blank.
berkeman said:
In the problem for this thread, the Relevant Equations/Information would be something like:

Parallel Lines: Have the same slope
Perpendicular Lines: Have inverse negative reciprocal slopes
Fixed that for you...

berkeman
Mark44 said:
Homework Statement: solve y = mx + b for b
For this trivial example, I'd be fine with leaving the Relevant Equations section blank.

Fixed that for you...
You are making a big deal about the HW Statement and Relevant Equations sections. Honestly, solving math problems is more important.

nycmathguy said:
You are making a big deal about the HW Statement and Relevant Equations sections.
Yes, because it shows us that you know exactly what the problem is, and what tools (equations, formulas, etc.) are going to be needed.

A case in point was your thread about proving that the diagonals of a parallelogram intersect at their midpoints. If you had written the formulas for distance between points and the midpoint of a line segment in the Relevant Equations section, that would have been strong evidence that you knew what to do. Since you didn't do so, helpers had to ask you if you knew both of these formulas.

nycmathguy said:
Honestly, solving math problems is more important.
Solving the problem is important, but without a clear understanding of what the problem is about, and the tools you can use to solve it, it's extremely unlikely that you'll be able to solve the problem.

1. What is the difference between parallel and perpendicular lines?

Parallel lines are two lines that are always the same distance apart and never intersect, while perpendicular lines intersect at a 90 degree angle.

2. How can I tell if two lines are parallel?

If two lines have the same slope, they are parallel. Another way to determine if two lines are parallel is to use the slope-intercept form of the equation and see if the slopes are equal.

3. Can two lines be both parallel and perpendicular?

No, two lines can only be either parallel or perpendicular, not both. Parallel lines have the same slope, while perpendicular lines have negative reciprocal slopes.

4. How do I find the equation of a line that is parallel or perpendicular to a given line?

To find the equation of a line that is parallel to a given line, use the same slope as the given line but a different y-intercept. To find the equation of a line that is perpendicular to a given line, use the negative reciprocal slope of the given line and a different y-intercept.

5. Are parallel and perpendicular lines important in real life?

Yes, parallel and perpendicular lines are important in many real-life applications such as architecture, engineering, and navigation. They are used to create and design structures, determine angles and distances, and create maps and graphs.

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