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

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

by Brent@GMATPrepNow » Wed Feb 03, 2021 10:26 am

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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

Answer: A
Source: Magoosh
Brent Hanneson - Creator of GMATPrepNow.com
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GMAT/MBA Expert

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Re: Line k is in the rectangular coordinate system. If line k is defined by the equation

by Brent@GMATPrepNow » Sun Feb 07, 2021 7:24 am
Brent@GMATPrepNow wrote: ↑
Wed Feb 03, 2021 10:26 am
 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

Answer: A
Source: Magoosh
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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