pappueshwar wrote:hi Mike,
request to explain this slope concept and y intercept concepts once again in regards with movement up , down and side ways... i am of the opinion that the slope should be read from the perspective of Y intercept
say the equation given is y = 1/2x - 2
so slope here is 1/2
y intercept is -2.
so when we want to plot this on the co-ordinate plane first place a point on -2, from there on since it is a positive slope, where in change in Y is 1 and change in X is 2 so u need to move 1 point up and 2 points right so the point is (2,-1) correct
in this case:
slope is -1/6
y intercept -6
so place the point on -6 (y-intercept), since the change in y is -1 the point moves down and moves right for change in X to 6 places making the point (6, -7).correct
let me know on this. i know i am wrong but i wanna get the concept right...
similar concept can be applied here and hence i arrived the answer as C. not correct
Dear
pappueshwar
You do understand the basic concept of slope quite well. The only thing I'll add, which may be obvious to you, is: a slope of 1/2 can mean
move right 2 and up 1, but it can equally well mean
move left 2 and down 1. Starting with a slope of 1/2 and a y-intercept of -2, moving to the right, we get:
(0, -2) --> (2, -1) --> (4, 0) --> (6, 1) etc.
and moving left, we get:
(0, -2) --> (-2, -3) --> (-4, -4) --> (-6, -5) etc.
I assume those ideas about slope also make sense.
Understanding slope itself is not a problem here. Let's talk about this particular question. Again, the question:
In the rectangular coordinate system shown above, does the line k (not shown) intersect quadrant II?
(1) The slope of k is -1/6
(2) The y-intercept of k is -6.
This is a tricky question.
Statement #1: We know the line has a negative slope, a slope of -1/6. We don't know the y-intercept. We want to know: does the line pass through QII? Well, if the y-intercept is a positive number, then the line definitely passes through QII. What if the y-intercept is negative? If the y-intercept is negative, the line definitely goes through QIII and QIV, but what about QI or QII?
Well, if the slope is negative, it goes down to the right and up to the left. In particular, as we go an infinite distance to the left, the line continues to rise without limit. That means, at some point, it must enter QII.
Another way to say it: every non-horizontal line has an x-intercept. Line k has slope of m = -1/6, so it definitely has to have an x-intercept. If the y-intercept is negative and the slope is negative, that means the x-intercept cannot occur on the positive x-axis --- it must occur on the negative x-axis. See diagram in the attached pdf. If line k has an x-intercept on the negative x-axis, that means it must enter QII.
Thus, statement #1, by itself, is
sufficient.
As I think you appreciated, statement #2, by itself, is
insufficient, so the correct answer is
A.
TAKEAWAY:
1) Any line with a positive slope, regardless of y-intercept, must go through QI and QIII
2) Any line with a negative slope, regardless of y-intercept, must go through QII and QIV
Does all this make sense? Please let me know if you have any further questions.
Mike
