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The slope intercept form of the linear equation is
- a)y = c⁄b - ax⁄b
- b)y = b⁄c - ax⁄b
- c)y = c⁄b - ab⁄x
- d)xy = bx⁄c - ay⁄b
Correct answer is option 'A'. Can you explain this answer?
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The slope intercept form of the linear equation isa)y = c⁄b - ax...
Understanding Slope-Intercept Form
The slope-intercept form of a linear equation is typically expressed as:
y = mx + b
where:
- **m** is the slope of the line,
- **b** is the y-intercept, the point where the line crosses the y-axis.
Analyzing the Given Options
Let's break down option 'A':
a) y = c/b - ax/b
To transform this into a recognizable form, we can rearrange the equation:
1. Start with the given equation:
y = c/b - ax/b
2. This can be rewritten by combining the terms:
y = - (a/b)x + (c/b)
Here, you can see that:
- The slope (m) is **-a/b**,
- The y-intercept (b) is **c/b**.
This matches the slope-intercept form \(y = mx + b\).
Why the Other Options are Incorrect
- **Option b:** y = b/c - ax/b does not conform to the slope-intercept because the slope isn't clearly defined.
- **Option c:** y = c/b - ab/x does not represent a linear equation since it has a term with x in the denominator.
- **Option d:** xy = bx/c - ay/b is not in slope-intercept form at all and represents a different equation entirely.
Conclusion
Thus, option 'A' correctly represents the slope-intercept form of a linear equation, confirming that the correct answer is indeed option 'A'. This understanding is crucial for solving linear equations effectively in the JEE examination.
The slope-intercept form of a linear equation is typically expressed as:
y = mx + b
where:
- **m** is the slope of the line,
- **b** is the y-intercept, the point where the line crosses the y-axis.
Analyzing the Given Options
Let's break down option 'A':
a) y = c/b - ax/b
To transform this into a recognizable form, we can rearrange the equation:
1. Start with the given equation:
y = c/b - ax/b
2. This can be rewritten by combining the terms:
y = - (a/b)x + (c/b)
Here, you can see that:
- The slope (m) is **-a/b**,
- The y-intercept (b) is **c/b**.
This matches the slope-intercept form \(y = mx + b\).
Why the Other Options are Incorrect
- **Option b:** y = b/c - ax/b does not conform to the slope-intercept because the slope isn't clearly defined.
- **Option c:** y = c/b - ab/x does not represent a linear equation since it has a term with x in the denominator.
- **Option d:** xy = bx/c - ay/b is not in slope-intercept form at all and represents a different equation entirely.
Conclusion
Thus, option 'A' correctly represents the slope-intercept form of a linear equation, confirming that the correct answer is indeed option 'A'. This understanding is crucial for solving linear equations effectively in the JEE examination.
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The slope intercept form of the linear equation isa)y = c⁄b - ax...
Ax+by+c=0
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The slope intercept form of the linear equation isa)y = c⁄b - ax⁄bb)y = b⁄c - ax⁄bc)y = c⁄b - ab⁄xd)xy = bx⁄c - ay⁄bCorrect answer is option 'A'. Can you explain this answer?
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