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Draw the graph of the linear equation 2 (X + 1) equals to 3 (y -1) - 4 and check whether point ( - 3 ,1) lies on the line?
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Draw the graph of the linear equation 2 (X + 1) equals to 3 (y -1) - 4...
Understanding the Equation
The given linear equation is:
2 (X + 1) = 3 (y - 1) - 4.
First, simplify the equation:
- Expand the left side:
2X + 2
- Expand the right side:
3y - 3 - 4 = 3y - 7
Now, equate both sides:
2X + 2 = 3y - 7.
Rearranging gives:
3y = 2X + 9,
y = (2/3)X + 3.
Graphing the Equation
To graph the equation y = (2/3)X + 3, follow these steps:
- Identify the **y-intercept**: (0, 3)
- Identify another point using the slope (2/3):
From (0, 3), move up 2 units and right 3 units to (3, 5).
Plot these points and draw a straight line through them.
Checking the Point (-3, 1)
To check if the point (-3, 1) lies on the line, substitute X = -3 into the equation:
y = (2/3)(-3) + 3
y = -2 + 3
y = 1.
Since the calculated y-value (1) equals the y-value of the point (-3, 1), the point lies on the line.
Conclusion
- The graph of the linear equation has been constructed.
- The point (-3, 1) is confirmed to lie on the line, demonstrating the relationship defined by the equation.
The given linear equation is:
2 (X + 1) = 3 (y - 1) - 4.
First, simplify the equation:
- Expand the left side:
2X + 2
- Expand the right side:
3y - 3 - 4 = 3y - 7
Now, equate both sides:
2X + 2 = 3y - 7.
Rearranging gives:
3y = 2X + 9,
y = (2/3)X + 3.
Graphing the Equation
To graph the equation y = (2/3)X + 3, follow these steps:
- Identify the **y-intercept**: (0, 3)
- Identify another point using the slope (2/3):
From (0, 3), move up 2 units and right 3 units to (3, 5).
Plot these points and draw a straight line through them.
Checking the Point (-3, 1)
To check if the point (-3, 1) lies on the line, substitute X = -3 into the equation:
y = (2/3)(-3) + 3
y = -2 + 3
y = 1.
Since the calculated y-value (1) equals the y-value of the point (-3, 1), the point lies on the line.
Conclusion
- The graph of the linear equation has been constructed.
- The point (-3, 1) is confirmed to lie on the line, demonstrating the relationship defined by the equation.
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Draw the graph of the linear equation 2 (X + 1) equals to 3 (y -1) - 4 and check whether point ( - 3 ,1) lies on the line?
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Draw the graph of the linear equation 2 (X + 1) equals to 3 (y -1) - 4 and check whether point ( - 3 ,1) lies on the line? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Draw the graph of the linear equation 2 (X + 1) equals to 3 (y -1) - 4 and check whether point ( - 3 ,1) lies on the line? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Draw the graph of the linear equation 2 (X + 1) equals to 3 (y -1) - 4 and check whether point ( - 3 ,1) lies on the line?.
Draw the graph of the linear equation 2 (X + 1) equals to 3 (y -1) - 4 and check whether point ( - 3 ,1) lies on the line? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Draw the graph of the linear equation 2 (X + 1) equals to 3 (y -1) - 4 and check whether point ( - 3 ,1) lies on the line? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Draw the graph of the linear equation 2 (X + 1) equals to 3 (y -1) - 4 and check whether point ( - 3 ,1) lies on the line?.
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