Which Of The Following Is The Equation Of A Line That Passes Through The Points \[$(0, 6)\$\] And \[$(2, 10)\$\]?A. \[$y = 2x + 6\$\] B. \[$y = 2x - 6\$\] C. \[$y = -2x - 6\$\] D. \[$y = -2x + 6\$\]

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Introduction

In mathematics, the equation of a line is a fundamental concept that is used to describe the relationship between two variables, typically x and y. The equation of a line can be expressed in various forms, including the slope-intercept form, point-slope form, and standard form. In this article, we will focus on finding the equation of a line that passes through two given points.

Understanding the Problem

We are given two points, (0, 6) and (2, 10), and we need to find the equation of a line that passes through these two points. To do this, we will use the point-slope form of a line, which is given by the equation:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

Finding the Slope

To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line. In this case, we have:

m = (10 - 6) / (2 - 0) m = 4 / 2 m = 2

Finding the Equation of the Line

Now that we have the slope, we can use the point-slope form of a line to find the equation of the line. We will use the point (0, 6) as the point (x1, y1) in the equation.

y - 6 = 2(x - 0) y - 6 = 2x y = 2x + 6

Evaluating the Options

Now that we have the equation of the line, we can evaluate the options given in the problem.

A. y = 2x + 6 B. y = 2x - 6 C. y = -2x - 6 D. y = -2x + 6

From our calculations, we can see that option A is the correct equation of the line.

Conclusion

In this article, we have shown how to find the equation of a line that passes through two given points. We used the point-slope form of a line and found the slope of the line using the formula. We then used the point-slope form to find the equation of the line. Finally, we evaluated the options given in the problem and found that option A is the correct equation of the line.

Key Takeaways

  • The equation of a line can be expressed in various forms, including the slope-intercept form, point-slope form, and standard form.
  • The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
  • The slope of a line can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
  • The equation of a line can be found using the point-slope form of a line, given the slope and a point on the line.

Frequently Asked Questions

  • Q: What is the equation of a line that passes through the points (0, 6) and (2, 10)? A: The equation of the line is y = 2x + 6.
  • Q: How do I find the slope of a line? A: You can find the slope of a line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
  • Q: What is the point-slope form of a line? A: The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

Further Reading

  • For more information on the equation of a line, see the article "The Equation of a Line: A Comprehensive Guide".
  • For more information on the point-slope form of a line, see the article "The Point-Slope Form of a Line: A Step-by-Step Guide".
  • For more information on the slope of a line, see the article "The Slope of a Line: A Comprehensive Guide".

Introduction

In our previous article, we discussed how to find the equation of a line that passes through two given points. We used the point-slope form of a line and found the slope of the line using the formula. We then used the point-slope form to find the equation of the line. In this article, we will answer some frequently asked questions related to the equation of a line.

Q: What is the equation of a line that passes through the points (0, 6) and (2, 10)?

A: The equation of the line is y = 2x + 6.

Q: How do I find the slope of a line?

A: You can find the slope of a line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Q: What is the point-slope form of a line?

A: The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

Q: How do I find the equation of a line that passes through a point and has a given slope?

A: You can use the point-slope form of a line to find the equation of the line. The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

Q: What is the slope-intercept form of a line?

A: The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept.

Q: How do I find the y-intercept of a line?

A: You can find the y-intercept of a line by substituting x = 0 into the equation of the line.

Q: What is the standard form of a line?

A: The standard form of a line is given by the equation Ax + By = C, where A, B, and C are constants.

Q: How do I find the equation of a line that passes through two points and has a given slope?

A: You can use the point-slope form of a line to find the equation of the line. The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

Q: What is the equation of a line that passes through the points (0, 0) and (2, 3)?

A: The equation of the line is y = (3/2)x.

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

A: You can use the point-slope form of a line to find the equation of the line. The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

Q: What is the equation of a line that passes through the points (0, 0) and (2, 4)?

A: The equation of the line is y = 2x.

Q: How do I find the equation of a line that passes through two points and is perpendicular to a given line?

A: You can use the point-slope form of a line to find the equation of the line. The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

Conclusion

In this article, we have answered some frequently asked questions related to the equation of a line. We have discussed how to find the equation of a line that passes through two given points, how to find the slope of a line, and how to find the equation of a line that passes through a point and has a given slope. We have also discussed the slope-intercept form, standard form, and point-slope form of a line.

Key Takeaways

  • The equation of a line can be expressed in various forms, including the slope-intercept form, point-slope form, and standard form.
  • The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
  • The slope of a line can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
  • The equation of a line can be found using the point-slope form of a line, given the slope and a point on the line.

Frequently Asked Questions

  • Q: What is the equation of a line that passes through the points (0, 6) and (2, 10)? A: The equation of the line is y = 2x + 6.
  • Q: How do I find the slope of a line? A: You can find the slope of a line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
  • Q: What is the point-slope form of a line? A: The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

Further Reading

  • For more information on the equation of a line, see the article "The Equation of a Line: A Comprehensive Guide".
  • For more information on the point-slope form of a line, see the article "The Point-Slope Form of a Line: A Step-by-Step Guide".
  • For more information on the slope of a line, see the article "The Slope of a Line: A Comprehensive Guide".