A Given Line Has The Equation 10 X + 2 Y = − 2 10x + 2y = -2 10 X + 2 Y = − 2 . What Is The Equation, In Slope-intercept Form, Of The Line That Is Parallel To The Given Line And Passes Through The Point (0, 12)?A. Y = − 5 X + 12 Y = -5x + 12 Y = − 5 X + 12 B. 5 X + Y = 12 5x + Y = 12 5 X + Y = 12 C. $y - 12

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Introduction

In the realm of mathematics, particularly in the domain of linear equations, understanding the concept of parallel lines is crucial. When two lines are parallel, they have the same slope but different y-intercepts. In this article, we will delve into the world of parallel lines and explore how to find the equation of a line that is parallel to a given line and passes through a specific point.

The Given Line: A Foundation for Understanding

The given line has the equation 10x+2y=−210x + 2y = -2. To understand this equation, we need to rewrite it in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. To do this, we need to isolate the variable yy on one side of the equation.

# Given equation
# 10x + 2y = -2

As we can see, the slope of the given line is −5-5, and the y-intercept is −1-1. This information will be crucial in finding the equation of the parallel line.

The Parallel Line: A New Equation with the Same Slope

Since the parallel line has the same slope as the given line, its slope is also −5-5. However, the y-intercept will be different. To find the equation of the parallel line, we need to use the point-slope form of a linear equation, which is y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope.

The Point: A Key to Unlocking the Equation

The point through which the parallel line passes is (0,12)(0, 12). We can use this point to find the equation of the parallel line.

# Point-slope form
# y - 12 = -5(x - 0)

As we can see, the equation of the parallel line is y=−5x+12y = -5x + 12. This equation is in slope-intercept form, and it has the same slope as the given line but a different y-intercept.

Conclusion

In conclusion, we have successfully found the equation of a line that is parallel to the given line and passes through the point (0,12)(0, 12). The equation of the parallel line is y=−5x+12y = -5x + 12. This equation is in slope-intercept form, and it has the same slope as the given line but a different y-intercept. Understanding the concept of parallel lines and how to find their equations is crucial in mathematics, particularly in the domain of linear equations.

Discussion

The equation of the parallel line is y=−5x+12y = -5x + 12. This equation is in slope-intercept form, and it has the same slope as the given line but a different y-intercept. The given line has the equation 10x+2y=−210x + 2y = -2, and its slope is −5-5. The parallel line has the same slope but a different y-intercept.

Answer

The correct answer is A. y=−5x+12y = -5x + 12.

Additional Information

  • The given line has the equation 10x+2y=−210x + 2y = -2.
  • The slope of the given line is −5-5.
  • The y-intercept of the given line is −1-1.
  • The parallel line has the same slope as the given line but a different y-intercept.
  • The equation of the parallel line is y=−5x+12y = -5x + 12.

References

Tags

  • Linear Equations
  • Parallel Lines
  • Slope-Intercept Form
  • Point-Slope Form
  • Mathematics

Introduction

In our previous article, we explored the concept of parallel lines and how to find the equation of a line that is parallel to a given line and passes through a specific point. We also provided a step-by-step solution to the problem. In this article, we will address some of the most frequently asked questions related to the topic.

Q&A

Q1: What is the slope of the given line?

A1: The slope of the given line is −5-5. This can be found by rewriting the equation of the line in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

Q2: What is the y-intercept of the given line?

A2: The y-intercept of the given line is −1-1. This can be found by rewriting the equation of the line in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

Q3: How do I find the equation of a line that is parallel to a given line and passes through a specific point?

A3: To find the equation of a line that is parallel to a given line and passes through a specific point, you need to use the point-slope form of a linear equation, which is y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope. You can then simplify the equation to find the slope-intercept form.

Q4: What is the equation of the parallel line?

A4: The equation of the parallel line is y=−5x+12y = -5x + 12. This can be found by using the point-slope form of a linear equation and substituting the values of the point and the slope.

Q5: Why is the equation of the parallel line in slope-intercept form?

A5: The equation of the parallel line is in slope-intercept form because it has been rewritten in the form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. This form is useful for understanding the relationship between the slope and the y-intercept of the line.

Q6: Can I use the point-slope form to find the equation of a line that is parallel to a given line and passes through a specific point?

A6: Yes, you can use the point-slope form to find the equation of a line that is parallel to a given line and passes through a specific point. This form is useful for finding the equation of a line that passes through a specific point and has a given slope.

Q7: What is the relationship between the slope and the y-intercept of a line?

A7: The relationship between the slope and the y-intercept of a line is that the slope is the coefficient of the x-term, and the y-intercept is the constant term. In the equation y=mx+by = mx + b, mm is the slope and bb is the y-intercept.

Q8: Can I use the slope-intercept form to find the equation of a line that is parallel to a given line and passes through a specific point?

A8: Yes, you can use the slope-intercept form to find the equation of a line that is parallel to a given line and passes through a specific point. This form is useful for understanding the relationship between the slope and the y-intercept of the line.

Conclusion

In conclusion, we have addressed some of the most frequently asked questions related to the topic of parallel lines and how to find the equation of a line that is parallel to a given line and passes through a specific point. We hope that this article has been helpful in clarifying any doubts you may have had.

Discussion

The equation of the parallel line is y=−5x+12y = -5x + 12. This equation is in slope-intercept form, and it has the same slope as the given line but a different y-intercept. The given line has the equation 10x+2y=−210x + 2y = -2, and its slope is −5-5. The parallel line has the same slope but a different y-intercept.

Answer

The correct answer is A. y=−5x+12y = -5x + 12.

Additional Information

  • The given line has the equation 10x+2y=−210x + 2y = -2.
  • The slope of the given line is −5-5.
  • The y-intercept of the given line is −1-1.
  • The parallel line has the same slope as the given line but a different y-intercept.
  • The equation of the parallel line is y=−5x+12y = -5x + 12.

References

Tags

  • Linear Equations
  • Parallel Lines
  • Slope-Intercept Form
  • Point-Slope Form
  • Mathematics