2x - 3y = 9
-3y = 9 - 2x
3y = 2x - 9
y = 2/3x - 9

Answer is C

APPROACH #1: Rewrite the equation in slope y-intercept form (y = mx + b, where m = slope)

Take: 2x − 3y = 9
Subtract 2x from both sides to get: -3y = -2x + 9
Divide both sides by -3 to get: y = (2/3)x - 3
At this point we can readily see that 2/3 is the slope of the line, and the y-intercept is -3
Answer: C


APPROACH #2: Find any two points on the line and then calculate the slope between those two points
For example, the point x = 6 and y = 1 [aka (6, 1)] is on the line since these values satisfy the equation of the line, 2x - 3y = 9
Likewise, the point x = 3 and y = -1 [aka (3, -1)] is also on the line

At this point we can apply the slope formula....
Slope = (-1 - 1)/(3 - 6) = -2/-3 = 2/3
Answer: C

Cheers,
Brent
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\(3y = 2x - 9\)

Or, \(y = 2/3x - 3\)

So, Slope of line is 2/3, Answer must be (C)
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Solution:

Isolating y, we have:

3y = 2x - 9

y = (2/3)x - 9

Thus, the slope is 2/3.

Alternate Solution:

When a linear equation is expressed in standard form as ax + by = c, the formula for the slope is given as -a/b. Thus, for the linear equation 2x - 3y = 9, the value of -a/b is -2/-3 = 2/3.

Answer: C
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