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Line k is in the rectangular coordinate system. If line k is defined by the eqautiion 3y=2x+6, and...

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by BTGmoderatorLU » Tue Apr 07, 2020 1:44 am
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Source: Magoosh

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

The OA is A
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Re: Line k is in the rectangular coordinate system. If line k is defined by the eqautiion 3y=2x+6, and...

by Brent@GMATPrepNow » Tue Apr 07, 2020 5:57 am
BTGmoderatorLU wrote: ↑
Tue Apr 07, 2020 1:44 am
 Source: Magoosh

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

The OA is A
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: Line k is in the rectangular coordinate system. If line k is defined by the eqautiion 3y=2x+6, and...

by swerve » Wed Apr 08, 2020 7:00 am
BTGmoderatorLU wrote: ↑
Tue Apr 07, 2020 1:44 am
 Source: Magoosh

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

The OA is A
At x-axis, coordinates are of the form \((x,0)\).
Therefore,
\(2x=6 \Longrightarrow x=-3\)
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Re: Line k is in the rectangular coordinate system. If line k is defined by the eqautiion 3y=2x+6, and...

by Scott@TargetTestPrep » Mon Apr 13, 2020 3:57 am
BTGmoderatorLU wrote: ↑
Tue Apr 07, 2020 1:44 am
 Source: Magoosh

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

The OA is A
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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