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Line k is in the rectangular coordinate system. If line k is defined

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Bunuel
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Line k is in the rectangular coordinate system. If line k is defined [#permalink] Line k is in the rectangular coordinate system. If line k is defined   24 Aug 2018, 00:21
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Line k is in the rectangular coordinate system. If line k is defined by the equation 3y = 2x + 6, and line k intersects the x-axis at point (a,b), then what is the value of a?

A. -3
B. -2
C. 0
D. 2
E. 3
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A
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BrentGMATPrepNow
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Re: Line k is in the rectangular coordinate system. If line k is defined [#permalink] Line k is in the rectangular coordinate system. If line k is defined   07 Apr 2020, 06:57
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Bunuel
Line k is in the rectangular coordinate system. If line k is defined by the equation 3y = 2x + 6, and line k intersects the x-axis at point (a,b), then what is the value of a?

A. -3
B. -2
C. 0
D. 2
E. 3

Key concept #1: All points on the x-axis have 0 as their y-coordinate
Key concept #2: If a point is on a line, then the x- and y-coordinates of that point must satisfy the equation of that line

Application of key concept #1: Since (a,b) lies on the x-axis, we know that b = 0, which means the point is (a, 0)

Application of key concept #2: If (a, 0) lies on the line, then it must be true that: 3(0) = 2a + 6
Simplify: 0 = 2a + 6
Subtract 6 from both sides: -6 = 2a
Solve: a = -3

Answer: A

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Re: Line k is in the rectangular coordinate system. If line k is defined [#permalink] Line k is in the rectangular coordinate system. If line k is defined   24 Aug 2018, 00:28
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Bunuel
Line k is in the rectangular coordinate system. If line k is defined by the equation 3y = 2x + 6, and line k intersects the x-axis at point (a,b), then what is the value of a?

A. -3
B. -2
C. 0
D. 2
E. 3

Intersection point of line k with x-axis at point (a,b). At x-axis y=0
So (a,b)=(a,0)

Given, 3y=2x+6
Or, 0=2a+6
Or, a=-3

Ans. (A)
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Re: Line k is in the rectangular coordinate system. If line k is defined [#permalink] Line k is in the rectangular coordinate system. If line k is defined   24 Aug 2018, 01:20
Bunuel
Line k is in the rectangular coordinate system. If line k is defined by the equation 3y = 2x + 6, and line k intersects the x-axis at point (a,b), then what is the value of a?

A. -3
B. -2
C. 0
D. 2
E. 3
At x axis
Co-ordinate are (x, 0)
Therefore,

2x=-6
x=-3

A

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Re: Line k is in the rectangular coordinate system. If line k is defined [#permalink] Line k is in the rectangular coordinate system. If line k is defined   10 Apr 2020, 03:50
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Bunuel
Line k is in the rectangular coordinate system. If line k is defined by the equation 3y = 2x + 6, and line k intersects the x-axis at point (a,b), then what is the value of a?

A. -3
B. -2
C. 0
D. 2
E. 3

Since (a, b) is the x-intercept of line k, the value of b would be zero, and we have:

0 = 2a + 6

-6 = 2a

-3 = a

Answer: A
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Re: Line k is in the rectangular coordinate system. If line k is defined [#permalink] Line k is in the rectangular coordinate system. If line k is defined   03 Jun 2020, 18:26
Bunuel
Line k is in the rectangular coordinate system. If line k is defined by the equation 3y = 2x + 6, and line k intersects the x-axis at point (a,b), then what is the value of a?

A. -3
B. -2
C. 0
D. 2
E. 3

I got the correct answer by solving another way:
I determined that the slope was 2/3 by dividing both sides by 3. That also yields y-intercept of 2. Knowing 2/3 to be the slope, I just subtracted 2 from y and 3 from x in the point (0,2) to determine that x=3 at the value of y=0.
I see that this is convoluted and took notes on everyone's (much easier) way of solving! But I want to pose this alternate method to ask if this is a sound strategy?
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BrentGMATPrepNow
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Re: Line k is in the rectangular coordinate system. If line k is defined [#permalink] Line k is in the rectangular coordinate system. If line k is defined   25 Nov 2020, 11:56
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chandlerrock

I got the correct answer by solving another way:
I determined that the slope was 2/3 by dividing both sides by 3. That also yields y-intercept of 2. Knowing 2/3 to be the slope, I just subtracted 2 from y and 3 from x in the point (0,2) to determine that x=3 at the value of y=0.
I see that this is convoluted and took notes on everyone's (much easier) way of solving! But I want to pose this alternate method to ask if this is a sound strategy?

That's a perfectly sound strategy!! Nice work!
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Re: Line k is in the rectangular coordinate system. If line k is defined [#permalink] Line k is in the rectangular coordinate system. If line k is defined   15 Feb 2024, 02:29
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Re: Line k is in the rectangular coordinate system. If line k is defined [#permalink]
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