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In the \(xy\)-plane, lines \(k\) and \(l\) intersect at the point \((1,1)\). Is the \(y\)-intercept of \(k\) greater than the \(y\)-intercept of \(l\)?

(1) The slope of \(k\) is less than the slope of \(l\). (2) The slope of \(l\) is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive.... so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value... At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of \(k\) is less than the slope of \(l\). As seen above y intercept of line l will be more than line k... Suff

(2) The slope of \(l\) is positive. we require to know slope of line k also Insuff

A

Thanks, chetan2u great response. I am trying to understand the relationship of the slope and y intercept. I think irrespective of the line is increasing or decreasing the slope defines lines steepness w.r.t the y -axis. Thus, as we increase the slope our y -intercept should increase. [considering both the line don't have a common intersecting point on the y-axis]. Please let me know if my understanding is correct?

Hi...

If you just take the absolute value, yes with change in x as constant, change in y will be as per your understanding..

The slope depends on change in value of both x and y. Numerator has change in y, so more the change more the slope Denominator has change in x, so less the change more the slope

But the slope can be of two types.. From left bottom to right top...... Both change in x and y will be POSITIVE, so slope is POSITIVE From left top to bottom right......Change in y is NEGATIVE and change in x will be POSITIVE, so slope is -/+= NEGATIVE even if the absolute value or steepness is MORE
_________________

In the \(xy\)-plane, lines \(k\) and \(l\) intersect at the point \((1,1)\). Is the \(y\)-intercept of \(k\) greater than the \(y\)-intercept of \(l\)?

(1) The slope of \(k\) is less than the slope of \(l\). (2) The slope of \(l\) is positive.

please see the attachment, let say Ml= -4 Mk= -6 then the slope of k is less than slope of L y intercept K is greater than L

so I think we need both statement to confirm. isn't it?

Bunuel or anyone, please correct me

If the slope of line L is -4 and the slope of line K is -6, the lines won't look like the way you've drawn. The will look like as below:

Oh yea, I mean the red line is K and the blue line is L so then, even the slope L is larger than slope K, y intercept of K is still larger than L am I correct? that means, statement 1 is not suff. we also need to know if it is positive slope or negative

Oh yea, I mean the red line is K and the blue line is L so then, even the slope L is larger than slope K, y intercept of K is still larger than L am I correct? that means, statement 1 is not suff. we also need to know if it is positive slope or negative

(1) says that the slope of \(k\) is less than the slope of \(l\). So, in my image BLUE line is K (slope -6) and the RED line is L (slope -4).

As you can see the y-intercept of K is greater than the y-intercept of L. For (1) the y-intercept of K will always be greater than the y-intercept of L.
_________________

Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]

Show Tags

19 Sep 2017, 09:00

chetan2u wrote:

nalinnair wrote:

In the \(xy\)-plane, lines \(k\) and \(l\) intersect at the point \((1,1)\). Is the \(y\)-intercept of \(k\) greater than the \(y\)-intercept of \(l\)?

(1) The slope of \(k\) is less than the slope of \(l\). (2) The slope of \(l\) is positive.

Hi,

An easy question if you are aware of the slopes....

slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase..

If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is -ive.... so for a point (1,1), a line intercepting above Y as 1, it is -ive and with increase in Y, the slope will have even lesser value... At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...

So the relation of y-intercept is dependent on slope.. lesser the slope higher is the intercept..

(1) The slope of \(k\) is less than the slope of \(l\). As seen above y intercept of line l will be more than line k... Suff

(2) The slope of \(l\) is positive. we require to know slope of line k also Insuff

A

Hi,

from (1) Shouldn't the value of y-intercept of K always be greater than the y-intercept of L?

Re: In the xy-plane, lines k and l intersect at the point (1,1). Is the y- [#permalink]

Show Tags

15 Oct 2017, 10:03

gary391 wrote:

We can write the equation of the line in slope-intercept form as follow: [Where M is the slope and C is the y-intercept]

For Line K : Yk = Mk.Xk +Ck For Line L : Yl = Ml.Xl + Cl

Now, since these lines intercept at (1,1), it must satisfy the equation

For Line K : 1 = Mk.1 +Ck For Line L : 1 = Ml.1 + Cl

=> Mk + Ck = Ml + Cl ------ (equation I)

Now, From Statement 1 - Mk > Ml. Thus, for equation I to hold true. Y intercept of line k must be less than Y intercept of line l (Ck < Cl). Therefore Statement 1 is Sufficient.

Statement 2: Is not sufficient as it doesn't provide information regarding the slope of line L.

You can further refine equation: 1 = Mk + ck => Mk = 1-Ck. Similarly, Ml = 1-Cl. Therefore, from statement 1, Mk < Ml => 1-Ck < 1 - Cl => Ck > Cl

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