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The coefficients a,b, c in the following linear equation of the form ax + by + c = 0 is of the equation  are
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?
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Understanding the Linear Equation
The given equation is in the form of ax + by + c = 0. To identify the coefficients, we need to rearrange the equation properly.
Given Equation
The equation provided is:
7/2 x + 5/4 y = -9
Rearranging the Equation
To express it in the standard form (ax + by + c = 0), we can move -9 to the left side of the equation:
7/2 x + 5/4 y + 9 = 0
Now, it fits the standard form where:
Identifying Coefficients
- Coefficient of x (a) = 7/2
- Coefficient of y (b) = 5/4
- Constant term (c) = 9
Analyzing the Options
Now, let’s analyze the options provided:
- a) 7/2, 5/4, -9
- b) -7/2, 5/4, -9
- c) 7/2, 5/4, 9
- d) -7/2, 5/4, 9
The correct coefficients from our rearrangement are:
- a = 7/2
- b = 5/4
- c = 9
Correct Answer
Thus, the correct coefficients are:
- a = 7/2
- b = 5/4
- c = 9
However, option 'd' states -7/2, 5/4, 9, which is incorrect.
The correct answer should reflect the positive values of a and c. Therefore, the correct answer should actually be option 'c' which is 7/2, 5/4, and 9.
Make sure to verify the signs and values while identifying coefficients!
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