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by HPengineer » Tue Dec 21, 2010 11:49 pm
Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?


a.) -3x +2y = 6
b.) 3x + 2y = -6
c.) 3x - 2y = 6
D.) 2x-3y = 6
e.) -2x -3y = 6




I tried solving this by finding the slope of the two points... then solving the answer choices to find one with similar slope.. However i got it wrong... Not sure if it was because of simple mistake because explanation uses a different method to solve.
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by N:Dure » Wed Dec 22, 2010 12:01 am
IMO A

a) y= 3/2 x + 3


slope = 3-0/0-(-2)= 3/2
y intercept is +3

if you plugin any of the points, you'll get the same results
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by Night reader » Wed Dec 22, 2010 12:01 am
HPengineer wrote:Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?


a.) -3x +2y = 6
b.) 3x + 2y = -6
c.) 3x - 2y = 6
D.) 2x-3y = 6
e.) -2x -3y = 6




I tried solving this by finding the slope of the two points... then solving the answer choices to find one with similar slope.. However i got it wrong... Not sure if it was because of simple mistake because explanation uses a different method to solve.
IOM A
equation for line k => y=ax+b where
If the x-intercept of line k is -2 => y=0 and find x-intercept with 0=ax+b where a=-2 and b=3 (the y-intercept is 3)
0=-2a+3, 2a=3, a=3/2 a where a is the slope
now equation for line k is y=3x/2+3 or 2y=3x+6
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by Rahul@gurome » Wed Dec 22, 2010 12:13 am
HPengineer wrote:Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?

a.) -3x +2y = 6
b.) 3x + 2y = -6
c.) 3x - 2y = 6
D.) 2x-3y = 6
e.) -2x -3y = 6
A straight line equation can be written in a special form which is known as "intercept form". The form of the equation looks like: (x/a) + (y/b) = 1 where a is the x-intercept and b is the y-intercept.

Thus required equation --> x/(-2) + y/3 = 1 => 3x - 2y = -6

The correct answer is A

Note: You can also use the "slope-intercept" form (i.e. y = mx + c) but in that case you have to solve for two unknowns m (the slope) and c (the y-intercept) as there are more than one options with same slope (or y-intercept). And I feel that will a bit more time than the above method.
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by HPengineer » Wed Dec 22, 2010 12:15 am
thanks guys... i simply tried to use the equation rise/run to find the slope between two points.. although i understand your approaches im still a bit confused as to why mine didnt work... in theory should it not?
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by N:Dure » Wed Dec 22, 2010 12:29 am
Rahul@gurome wrote:
HPengineer wrote:Line k is in the rectangular coordinate system. If the x-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?

a.) -3x +2y = 6
b.) 3x + 2y = -6
c.) 3x - 2y = 6
D.) 2x-3y = 6
e.) -2x -3y = 6
you have to solve for two unknowns m (the slope) and c (the y-intercept) as there are more than one options with same slope (or y-intercept). And I feel that will a bit more time than the above method.
Not needed.

If you do the slope, you can eliminate choices b c d e. Since it's 3/2 & y intercept is given as 3, only A works.
Last edited by N:Dure on Wed Dec 22, 2010 12:44 am, edited 1 time in total.
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by Rahul@gurome » Wed Dec 22, 2010 12:36 am
HPengineer wrote:thanks guys... i simply tried to use the equation rise/run to find the slope between two points.. although i understand your approaches im still a bit confused as to why mine didnt work... in theory should it not?
Why not?
We have two points on the line (-2, 0) and (0,3).
Thus, rise = (3 - 0) = 3 and run = (0 - (-2)) = 2 => Slope = rise/run = 3/2

Now there are two options (A and C) with the same slope. Thus only with the slope we cannot uniquely determine the equation. We have to put one of those points in the equation y = mx + c, where m = 3/2 and solve for c.

Let's put (0, 3) on the equation: 3 = 0 + c => c = 3
Thus the required equation: y = (3/2)x + 3 => 2y = 3x + 6 => -3x + 2y = 6
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by Rahul@gurome » Wed Dec 22, 2010 12:44 am
N:Dure wrote:If you do the slope, you can eliminate choices b c d e. Since it's 3/2 only A works.
Option A : -3x +2y = 6 => 2y = 3x + 6 => y = (3/2)x + 3 => Slope = 3/2
Option C : 3x - 2y = 6 => 2y = 3x - 6 => y = (3/2)x - 3 => Slope = 3/2
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by N:Dure » Wed Dec 22, 2010 12:52 am
But the y-intercept in option c is -3 so it doesn't fit. It has to be 3 as given.
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