Good DS question - Cogeo II

[austin]

What is the slope of line p?
1. The x-intercept is twice the y intercept
2. The line passes through I and III quadrants

OA in a bit

[nervesofsteel]

C for me...

A) insufficient as if line passes through (0,1) and ( -2,0) slope is 1/2
id it passe through (0,1) and (2,0) the slope becomes -1/2.. so insufficient..

B) Line passing through quads cannot give an idea about slope...

if line passes through I and III quad.. and intercept on X axis is double the intercept on Y axis..then slope must be 1/2...

[anshulseth]

Lets use a generic eq of a line:
y=mx+c

If X-intercept = 2*Y-intercept

X-Intercept = -c/m
Y-Intercept = c

So, as per Stmt I: -c/m=2c
or m =-1/2

Sufficient.

Stmt II: we just know line passes thro center.
No more info.
Insufficient

Thus, A is the answer.

[ketkoag]

C for me as well.
by statement 1 slope can be negative or positive. hence insufficient.
by (2) we cannot find the actual value. hence insufficient.
Combining both, we get the slope as 1/2. hence sufficient.

[bluementor]

One more vote for A, same reasoning as anshulseth....

A) insufficient as if line passes through (0,1) and ( -2,0) slope is 1/2

I don't think this satisfies the condition in statement 1.

Statement 1 simply says:

c = 2*(-c/m), which is sufficient to answer for m. Hence A.

-BM-

[sanju09]

Slope of a line = - y-intercept/x-intercept.

For (1) x-intercept = 2 × y intercept, slope can be answered.

For (2) if the line passes through I and III quadrants along with passing through II or IV quadrant as well, or along with passing through the origin (no intercepts are possible in this case), the slope must be positive; but what exactly will be the value? No answer.

Take A from me.

[cubicle_bound_misfit]

Just one question to all the gurus.
Is there any way to find out that if a straight line goes thru I and III quad, and if x-intercept is twice y-intercept then, how many solutions possible?

[austin]

If a line passes through the first and third quadrants, the slope of the line could be +ve or -ve. The correct answer to this question is C.

NOTE: For a line passing thru 1 and 3 quad, slope is +ve
For a line passing thru 2 and 4 quad, slope is -ve

[bluementor]

I don't quite understand how C can be the answer.

We know that:

slope = - (y-intercept)/(x-intercept)

Statement 1 tells us that:

x-intercept = 2 * (y-intercept) ,

which is enough to answer the question. This also certainly proves that the slope can only be -1/2. So why not A?

-BM-

[Uri]

why do we need (2) for the statement to be true? (1) alone provides us with the solution So, answer should be (A).

C for me...

A) insufficient as if line passes through (0,1) and ( -2,0) slope is 1/2
id it passe through (0,1) and (2,0) the slope becomes -1/2.. so insufficient..

for (0,1) and (-2,0) the x-intercept is -2 times the y-intercept. if intercept means absolute value, then this would be correct. otherwise, (1) is sufficient. so, can any expert please help us with the answer?


austin, , can you please tell us the source of this question?

[austin]

When we say intercept of three, the distance from (0,0) is 3...but, is it in the positive or negative direction???

If a line passes through (3,0) or (-3,0), the intercept is still 3.. but the slopes could be different....

TRY YOURSELF: You can draw two lines: one through (3,0) and the other through (-3,0) with x-intercept twice the y intercept... The slope is 1/2 in one case and -1/2 the other case....

NOTE: If the angle made by the line with the +ve direction of the x-axis is acute (<90), then slope = tan (angle) = +ve (tan is +ve in first quadrant)

If the angle made by the line with the +ve direction of the x-axis is obtuse (>90), then slope = tan (angle) = -ve (tan is -ve in second quadrant)

SO WE NEED TO THROUGH WHICH QUADRANTs THE LINE PASSES THROUGH.

[austin]

I am quoting fleurdelisse's question and the discussion link here:

In the rectangular coordinate, does line k interest quandrant II? (quandrant II being the quandrant where x<0 and y>0)
(1) slope of k is -1/6
(2) y-intercept of k is -6

https://www.beatthegmat.com/line-and-slope-t35149.html

This, I think will help you understand the concept of intercept....

Observe statement 2: y intercept is -6. This means the line cuts at (0,-6).

[bluementor]

austin, thanks for responding.

Pls correct me if i am wrong, but the way i see it your explanation is contradictory.

In this post you mentioned:

When we say intercept of three, the distance from (0,0) is 3...but, is it in the positive or negative direction???

If a line passes through (3,0) or (-3,0), the intercept is still 3.. but the slopes could be different....

Here you are basically treating the intercept value as an absolute. If the y-intercept of a line is 3, then it could be intersecting the y-axis at (0,3) or (0,-3).

However, in the following post:

Observe statement 2: y intercept is -6. This means the line cuts at (0,-6).

Here you acknowledge that the sign of the y-intercept corresponds directly to a single point on the y-axis.

So which is it? I believe the later is true. If the y-intercept is 3, then the line can ONLY intersect (0,3), and NOT (0,-3). This is the reason why I feel statement 1 alone is sufficient to answer the original question in this post.

-BM-

[austin]

When we say intercept of 3, it means distance is 3...

We either say intercept of 3 in the negative direction of x-axis or say intercept is -3....both mean it passes thru (-3,0)

I used the latter example (fleurdelisse's problem) to convey that when you use the intercept to determine the slope you need to be careful....

"Making an intercept of 3" is different from "making an intercept of 3 with the positive direction of x-axis".. the latter is much more explicit.. the former is a bit tricky... the line can pass thru (3,0) or (-3,0) leading to different slopes and still we say intercept is 3....

[Ian Stewart]

What is the slope of line p?
1. The x-intercept is twice the y intercept
2. The line passes through I and III quadrants

OA in a bit

I'm also curious about the source. I'm going with E here, on a technicality. If the x-intercept and y-intercept are both zero, then the x-intercept is certainly two times the y-intercept, and as long as the slope is positive, the second statement will be true. So using both statements, the slope could be any positive number.

That's the only way to get the statements to agree, in fact; if the intercepts of line p are non-zero, then Statement 1 and Statement 2 are contradictory (Statement 1 guarantees the slope is negative, while Statement 2 guarantees the slope is positive).

We don't need any specialized formulas to analyze Statement 1, incidentally. Say the y-intercept of the line is (0,b), where b is nonzero. Then the x-intercept is (2b, 0), according to Statement 1. So the slope is:

(b - 0)/(0 - 2b) = -1/2

That will be true as long as b is not zero.