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Question 16528: Can anyone help me solve this?
If the line Kx - 2y = 6 has the same x and y-intercept, what is the value of K?
I'm not sure what to do with this.
I substituted zero for x and got
-2y = 6
y = -3
which would mean a set of points (0,-3) but how would that be the same
intercept for both x and y.
Any help would be very appreciated.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Perhaps a little common sense is required for this problem.
If a line has the same x- and y-intercept, then the line has a negative slope and the slope must be -1.
How can we say this? If the line had a positive slope the x-intercept would have the opposite sign of the y-intercept, unless, of course, it crossed at the origin.
Now if the x- and y-intercepts are the same value (both positive or both negative), then the line must have a negative slope and, since slope is defined as rise over run, the rise and the run are equal (in absolute value), ergo, the slope is -1.
But how does this find the value of K?
Well, let;s put your equation into the slope-intercept form.
Kx - 2y = 6 Add 2y to both sides.
Kx = 2y + 6 Subtract 6 from both sides.
Kx - 6 = 2y Divide both sides by 2.
y = (K/2)x - 6 The slope, m = K/2 = -1, So K = -2
The given line is:
y = (-1)x - 6
The x-intercept is: 0 = -x - 6, so x = -6
The y-intercept is: y = 0 - 6, so y = -6
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