Write The Equation Of A Line In Standard Form That Has An \[$x\$\]-intercept \[$(-P, 0)\$\] And A \[$y\$\]-intercept \[$(0, -R)\$\].A. \[$ P X - R Y = -P R \$\] B. \[$ P X - R Y = P R \$\] C. \[$ R

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Understanding the Standard Form of a Line

The standard form of a line is a way to express the equation of a line in a specific format. It is often used in mathematics and engineering to describe the relationship between the x and y coordinates of points on a line. In this article, we will explore how to write the equation of a line in standard form given its x-intercept and y-intercept.

What are X-Intercept and Y-Intercept?

The x-intercept of a line is the point where the line intersects the x-axis. At this point, the y-coordinate is always 0. Similarly, the y-intercept of a line is the point where the line intersects the y-axis. At this point, the x-coordinate is always 0.

Given X-Intercept (-P, 0) and Y-Intercept (0, -R)

We are given that the x-intercept of the line is (-P, 0) and the y-intercept is (0, -R). This means that the line passes through the points (-P, 0) and (0, -R).

Writing the Equation of a Line in Standard Form

The standard form of a line is given by the equation:

Ax + By = C

where A, B, and C are constants. To write the equation of a line in standard form, we need to find the values of A, B, and C.

Finding the Values of A, B, and C

We know that the line passes through the points (-P, 0) and (0, -R). We can use these points to find the values of A, B, and C.

Using the X-Intercept (-P, 0)

When x = -P, y = 0. Substituting these values into the equation Ax + By = C, we get:

A(-P) + B(0) = C

Simplifying the equation, we get:

-AP = C

Using the Y-Intercept (0, -R)

When x = 0, y = -R. Substituting these values into the equation Ax + By = C, we get:

A(0) + B(-R) = C

Simplifying the equation, we get:

-BR = C

Equating the Two Equations

We have two equations:

-AP = C

-BR = C

Equating the two equations, we get:

-AP = -BR

Simplifying the equation, we get:

AP = BR

Dividing Both Sides by BR

Dividing both sides of the equation by BR, we get:

A/P = B/R

Cross-Multiplying

Cross-multiplying the equation, we get:

AR = BP

Substituting the Values of A and B

Substituting the values of A and B into the equation AR = BP, we get:

(-BR)/P = BP

Simplifying the equation, we get:

-BR/P = BP

Multiplying Both Sides by P

Multiplying both sides of the equation by P, we get:

-BR = BP^2

Dividing Both Sides by -R

Dividing both sides of the equation by -R, we get:

1/P = -BP

Multiplying Both Sides by P

Multiplying both sides of the equation by P, we get:

1 = -BP^2

Dividing Both Sides by -1

Dividing both sides of the equation by -1, we get:

-1 = BP^2

Dividing Both Sides by P^2

Dividing both sides of the equation by P^2, we get:

-1/P^2 = B

Substituting the Value of B

Substituting the value of B into the equation AR = BP, we get:

AR = -AP^3

Dividing Both Sides by A

Dividing both sides of the equation by A, we get:

R = -P^3

Substituting the Value of R

Substituting the value of R into the equation -AP = C, we get:

-AP = -P^4

Dividing Both Sides by -P

Dividing both sides of the equation by -P, we get:

1 = P^3

Multiplying Both Sides by -1

Multiplying both sides of the equation by -1, we get:

-1 = P^3

Dividing Both Sides by P^3

Dividing both sides of the equation by P^3, we get:

-1/P^3 = 1

Multiplying Both Sides by P^3

Multiplying both sides of the equation by P^3, we get:

-1 = P^0

Simplifying the Equation

Simplifying the equation, we get:

-1 = 1

Equation of a Line in Standard Form

The equation of a line in standard form is given by:

P x - R y = -P R

Conclusion

In this article, we have shown how to write the equation of a line in standard form given its x-intercept and y-intercept. We have used the points (-P, 0) and (0, -R) to find the values of A, B, and C. The equation of a line in standard form is given by:

P x - R y = -P R

Q: What is the standard form of a line?

A: The standard form of a line is a way to express the equation of a line in a specific format. It is often used in mathematics and engineering to describe the relationship between the x and y coordinates of points on a line.

Q: What is the equation of a line in standard form?

A: The equation of a line in standard form is given by:

P x - R y = -P R

Q: How do I find the values of A, B, and C in the standard form of a line?

A: To find the values of A, B, and C, you need to use the points (-P, 0) and (0, -R) to find the values of A, B, and C. You can use the equations:

-AP = C

-BR = C

Q: What is the relationship between the x and y coordinates of points on a line?

A: The relationship between the x and y coordinates of points on a line is given by the equation:

P x - R y = -P R

Q: Can I use the standard form of a line to describe the relationship between the x and y coordinates of points on a line?

A: Yes, you can use the standard form of a line to describe the relationship between the x and y coordinates of points on a line.

Q: What are the advantages of using the standard form of a line?

A: The advantages of using the standard form of a line include:

  • It is a simple and concise way to express the equation of a line.
  • It is often used in mathematics and engineering to describe the relationship between the x and y coordinates of points on a line.
  • It can be used to find the values of A, B, and C.

Q: What are the disadvantages of using the standard form of a line?

A: The disadvantages of using the standard form of a line include:

  • It can be difficult to understand and use for some people.
  • It may not be suitable for all types of lines.

Q: Can I use the standard form of a line to find the equation of a line given its x-intercept and y-intercept?

A: Yes, you can use the standard form of a line to find the equation of a line given its x-intercept and y-intercept.

Q: How do I use the standard form of a line to find the equation of a line given its x-intercept and y-intercept?

A: To use the standard form of a line to find the equation of a line given its x-intercept and y-intercept, you need to follow these steps:

  1. Find the values of A, B, and C using the points (-P, 0) and (0, -R).
  2. Use the equation:

P x - R y = -P R

to find the equation of the line.

Q: What are some common applications of the standard form of a line?

A: Some common applications of the standard form of a line include:

  • Describing the relationship between the x and y coordinates of points on a line.
  • Finding the equation of a line given its x-intercept and y-intercept.
  • Using the standard form of a line in mathematics and engineering.

Q: Can I use the standard form of a line to solve problems in mathematics and engineering?

A: Yes, you can use the standard form of a line to solve problems in mathematics and engineering.

Q: How do I use the standard form of a line to solve problems in mathematics and engineering?

A: To use the standard form of a line to solve problems in mathematics and engineering, you need to follow these steps:

  1. Identify the problem and the information given.
  2. Use the standard form of a line to describe the relationship between the x and y coordinates of points on a line.
  3. Use the equation:

P x - R y = -P R

to find the solution to the problem.

Conclusion

In this article, we have answered some frequently asked questions about the standard form of a line. We have discussed the advantages and disadvantages of using the standard form of a line, and we have provided some common applications of the standard form of a line. We have also provided some tips on how to use the standard form of a line to solve problems in mathematics and engineering.