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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
A. −2
B. -2/3
C. 2/3
D. 3/2
E. 2
28 Apr 2017, 11:34
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2x - 3y = 9
-3y = 9 - 2x
3y = 2x - 9
y = 2/3x - 9
Answer is C
-3y = 9 - 2x
3y = 2x - 9
y = 2/3x - 9
Answer is C
03 Mar 2020, 09:01
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SajjadAhmad
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
A. −2
B. -2/3
C. 2/3
D. 3/2
E. 2
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
