What Is The Equation Of The Line That Passes Through The Points $(-2,2)$ And $(0,5)$?A. \$y = X + 5$[/tex\] B. $y = X - 5$ C. $y = -\frac{3}{2}x + 5$ D. \$y = \frac{3}{2}x +

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Introduction

In mathematics, finding the equation of a line that passes through two given points is a fundamental concept in algebra and geometry. The equation of a line can be determined using the slope-intercept form, which is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In this article, we will explore how to find the equation of a line that passes through the points (-2,2) and (0,5).

Understanding the Slope-Intercept Form

The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line is a measure of how steep the line is, and it can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Finding the Slope of the Line

To find the equation of the line that passes through the points (-2,2) and (0,5), we need to calculate the slope of the line. Using the formula m = (y2 - y1) / (x2 - x1), we can substitute the given points into the formula to get:

m = (5 - 2) / (0 - (-2)) m = 3 / 2 m = 1.5

Finding the Y-Intercept of the Line

Now that we have the slope of the line, we can use one of the given points to find the y-intercept of the line. We will use the point (0,5) to find the y-intercept. Substituting the point into the equation y = mx + b, we get:

5 = (3/2)(0) + b 5 = b

Writing the Equation of the Line

Now that we have the slope and the y-intercept of the line, we can write the equation of the line in slope-intercept form. Substituting the values of m and b into the equation y = mx + b, we get:

y = (3/2)x + 5

Conclusion

In conclusion, the equation of the line that passes through the points (-2,2) and (0,5) is y = (3/2)x + 5. This equation can be used to determine the y-coordinate of any point on the line, given the x-coordinate.

Discussion

The equation of a line can be determined using the slope-intercept form, which is given by y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this article, we used the points (-2,2) and (0,5) to find the equation of the line.

Frequently Asked Questions

  • What is the slope-intercept form of a line? The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
  • How do you find the slope of a line? The slope of a line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
  • How do you find the y-intercept of a line? The y-intercept of a line can be found by substituting one of the given points into the equation y = mx + b.

References

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Introduction

Finding the equation of a line that passes through two given points is a fundamental concept in algebra and geometry. In our previous article, we explored how to find the equation of a line that passes through the points (-2,2) and (0,5). In this article, we will answer some frequently asked questions related to finding the equation of a line.

Q&A

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

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

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

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

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

A: The y-intercept of a line can be found by substituting one of the given points into the equation y = mx + b.

Q: What is the equation of a line that passes through the points (1,3) and (2,5)?

A: To find the equation of the line that passes through the points (1,3) and (2,5), we need to calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points into the formula, we get:

m = (5 - 3) / (2 - 1) m = 2 / 1 m = 2

Now that we have the slope of the line, we can use one of the given points to find the y-intercept of the line. We will use the point (1,3) to find the y-intercept. Substituting the point into the equation y = mx + b, we get:

3 = (2)(1) + b 3 = 2 + b b = 1

Now that we have the slope and the y-intercept of the line, we can write the equation of the line in slope-intercept form. Substituting the values of m and b into the equation y = mx + b, we get:

y = 2x + 1

Q: What is the equation of a line that passes through the points (-3,4) and (0,2)?

A: To find the equation of the line that passes through the points (-3,4) and (0,2), we need to calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points into the formula, we get:

m = (2 - 4) / (0 - (-3)) m = -2 / 3 m = -0.67

Now that we have the slope of the line, we can use one of the given points to find the y-intercept of the line. We will use the point (0,2) to find the y-intercept. Substituting the point into the equation y = mx + b, we get:

2 = (-2/3)(0) + b 2 = b

Now that we have the slope and the y-intercept of the line, we can write the equation of the line in slope-intercept form. Substituting the values of m and b into the equation y = mx + b, we get:

y = (-2/3)x + 2

Q: How do you find the equation of a line that passes through three points?

A: To find the equation of a line that passes through three points, we need to calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1). We can use any two of the three points to calculate the slope. Once we have the slope, we can use one of the three points to find the y-intercept of the line.

Conclusion

In conclusion, finding the equation of a line that passes through two given points is a fundamental concept in algebra and geometry. We have answered some frequently asked questions related to finding the equation of a line, including how to find the slope and y-intercept of a line, and how to write the equation of a line in slope-intercept form.

Discussion

Finding the equation of a line that passes through two given points is a fundamental concept in algebra and geometry. In this article, we have answered some frequently asked questions related to finding the equation of a line. We hope that this article has been helpful in understanding how to find the equation of a line.

Frequently Asked Questions

  • What is the slope-intercept form of a line? The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
  • How do you find the slope of a line? The slope of a line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
  • How do you find the y-intercept of a line? The y-intercept of a line can be found by substituting one of the given points into the equation y = mx + b.

References

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