Problem Solving

M7MBA wrote:What is the slope of the line defined by the equation \(2x − 3y = 9?\)

A. −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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M7MBA wrote:What is the slope of the line defined by the equation \(2x − 3y = 9?\)

A. −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