Lines k and m are parallel to each other. Is the slope of

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Lines k and m are parallel to each other. Is the slope of line k positive?

(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).


In the original condition, there are 4 variables(x1, x2, y1, y2) from the slope=(y2-y1)/(x2-x1). (There are 2 lines, which makes 8 variables. However, since the lines are parallel, which makes 4 variables) In order to match with the number of equations, you need 4 equations, which is likely to make E the answer.
When 1) & 2), you cannot figure out the slope of either line k or line m in a unique way, which is not sufficient.
Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

If i go by the defination of parallel lines : Parallel lines are two lines that are always the same distance apart and never touch.

if i take into consideration both option then both lines have a common intercept on Y-axis that is 2 so how come the two lines are parallel to each other ?

One of the infinitely many possible cases is given below:


If you rotate both lines simultaneously you'll get other cases.

Target question: Is the slope of line k positive?

Given: Lines k and m are parallel to each other.

Let's jump straight to....

Statements 1 and 2 combined
There are many cases that satisfy BOTH statements. Here are two:

Case a:

In this case, the slope of line k is POSITIVE


Case b:

In this case, the slope of line k is NEGATIVE

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

We are given that lines k and m are parallel to each other, and when two lines are parallel, they have the same slope. We must determine whether the slope of line k is positive.

Statement One Alone:

Line k passes through the point (3, 2).

Using the information in statement one, the slope of line k can be positive or negative. An infinite number of lines can pass through the point (3, 2), some of which have positive slopes and some of which have negative slopes. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

Line m passes through the point (-3, 2).

Using the information in statement two, we know that the slope of line m can be positive or negative. An infinite number of lines can pass through the point (-3, 2), some of which have positive slopes and some of which have negative slopes. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we know that line k passes through (3, 2) and line m passes through (-3, 2). However, we still do not have enough information to determine whether the slope of line k is positive or negative, since both lines can have positive slopes or both can have negative slopes.
Thus, statements one and two together are not sufficient to answer the question.

Answer: E

Answer: Option E

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