What is the slope of the line defined by the equation

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Tue Apr 30, 2019 12:45 am

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What is the slope of the line defined by the equation $2x âˆ’ 3y = 9?$

A. âˆ’2
B. -2/3
C. 2/3
D. 3/2
E. 2

[spoiler]OA=C[/spoiler]

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Tue Apr 30, 2019 12:45 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Apr 30, 2019 8:37 pm

M7MBA wrote:What is the slope of the line defined by the equation $2x âˆ’ 3y = 9?$

A. âˆ’2
B. -2/3
C. 2/3
D. 3/2
E. 2

[spoiler]OA=C[/spoiler]

Source: Princeton Review

Slope of a line is m for a linear equation $y = mx + c$

So, let's manipulate the equation of the line $2x - 3y = 9$ into $y = mx + c$.

$2x - 3y = 9$ => $-3y = 9-2x$ => $y = \frac {9}{-3} - \frac {2x}{-3}$ => $y = -3 + \frac {2}{3}x$

Thus, slope = 2/3

The correct answer: C

Hope this helps!

-Jay
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swerve: Legendary Member; Posts: 2560; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Thu May 02, 2019 9:29 am

$$\begin{align}
2x - 3y &= 9 \\
-3y &= 9 - 2x \\
3y &= 2x - 9 \\
y &= \frac{2}{3}x - 9
\end{align}$$

Therefore, the answer is __C__

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8178; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu May 02, 2019 4:20 pm

M7MBA wrote:What is the slope of the line defined by the equation $2x âˆ’ 3y = 9?$

A. âˆ’2
B. -2/3
C. 2/3
D. 3/2
E. 2

[spoiler]OA=C[/spoiler]

Source: Princeton Review

Rewriting the equation in slope-intercept form, we have:

-3y = -2x + 9

y = (-2/-3)x + 9/-3

y = (2/3)x - 3

We see that the slope is 2/3.

Answer: C

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