Convert to a Single Fraction

Oct 13, 2025 by miodeya.com 30 views

Introduction

In mathematics, a line is a set of points that extend infinitely in two directions. It is defined by two points, and its equation can be determined using various methods. In this article, we will explore how to find the equation of a line with a given gradient, using the point-slope form of a linear equation.

The Point-Slope Form

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

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

Given Information

Ida drew a line passing through the point (-2, -1). The line has a gradient of 1 1/4, which can be written as a fraction: 5/4.

Step 1: Write the Point-Slope Form

Using the point-slope form, we can write the equation of the line as:

y - (-1) = (5/4)(x - (-2))

Simplify the Equation

To simplify the equation, we can start by evaluating the expressions inside the parentheses:

y + 1 = (5/4)(x + 2)

Distribute the Gradient

Next, we can distribute the gradient to the terms inside the parentheses:

y + 1 = (5/4)x + (5/4)(2)

Simplify Further

We can simplify the equation further by evaluating the expression (5/4)(2):

y + 1 = (5/4)x + 5/2

Combine Like Terms

To combine like terms, we can rewrite the equation as:

y + 1 = (5/4)x + 5/2

Convert to a Single Fraction

We can convert the terms to a single fraction by finding a common denominator:

y + 1 = (5/4)x + 10/4

Simplify the Equation

Finally, we can simplify the equation by combining the terms:

y + 1 = (5/4)x + 10/4

The Final Equation

The final equation of the line is:

y = (5/4)x - 9/4

Conclusion

In this article, we have explored how to find the equation of a line with a given gradient, using the point-slope form of a linear equation. We have used the point-slope form to write the equation of the line, simplified the equation, and finally obtained the final equation of the line.

Key Takeaways

The point-slope form of a linear equation is given by: y - y1 = m(x - x1)
The equation of a line can be determined using the point-slope form
The gradient of a line can be written as a fraction
The equation of a line can be simplified by distributing the gradient and combining like terms

References

[1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f-linear-equations
[2] Mathway. (n.d.). Linear Equations. Retrieved from https://www.mathway.com/subjects/linear-equations
[3] Wolfram MathWorld. (n.d.). Linear Equations. Retrieved from https://mathworld.wolfram.com/LinearEquation.html
Ida's Line: A Q&A Guide to Finding the Equation of a Line with a Given Gradient ====================================================================

Introduction

In our previous article, we explored how to find the equation of a line with a given gradient, using the point-slope form of a linear equation. In this article, we will answer some frequently asked questions about finding the equation of a line with a given gradient.

Q&A

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

A: The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

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

Q: How do I find the equation of a line with a given gradient?

A: To find the equation of a line with a given gradient, you can use the point-slope form of a linear equation. First, identify a point on the line, and then use the gradient to write the equation of the line.

Q: What is the gradient of a line?

A: The gradient of a line is a measure of how steep the line is. It can be written as a fraction, and it is used to determine the equation of the line.

Q: How do I simplify the equation of a line?

A: To simplify the equation of a line, you can start by distributing the gradient to the terms inside the parentheses. Then, combine like terms and simplify the equation further.

Q: What is the final equation of a line?

A: The final equation of a line is the simplified equation that you obtain after distributing the gradient and combining like terms.

Q: Can I use the point-slope form to find the equation of a line with a given point and gradient?

A: Yes, you can use the point-slope form to find the equation of a line with a given point and gradient. Simply substitute the values of the point and the gradient into the point-slope form, and then simplify the equation.

Q: What are some common mistakes to avoid when finding the equation of a line with a given gradient?

A: Some common mistakes to avoid when finding the equation of a line with a given gradient include:

Not distributing the gradient to the terms inside the parentheses
Not combining like terms
Not simplifying the equation further
Not using the correct point-slope form

Q: How do I check my work when finding the equation of a line with a given gradient?

A: To check your work when finding the equation of a line with a given gradient, you can substitute the values of the point and the gradient into the equation and see if it is true. You can also use a graphing calculator or a computer program to graph the line and check if it is correct.

Conclusion

In this article, we have answered some frequently asked questions about finding the equation of a line with a given gradient. We have covered topics such as the point-slope form, the gradient of a line, and how to simplify the equation of a line. We hope that this article has been helpful in answering your questions and providing you with a better understanding of how to find the equation of a line with a given gradient.

Key Takeaways

The point-slope form of a linear equation is given by: y - y1 = m(x - x1)
The equation of a line can be determined using the point-slope form
The gradient of a line can be written as a fraction
The equation of a line can be simplified by distributing the gradient and combining like terms
The final equation of a line is the simplified equation that you obtain after distributing the gradient and combining like terms

References

[1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f-linear-equations
[2] Mathway. (n.d.). Linear Equations. Retrieved from https://www.mathway.com/subjects/linear-equations
[3] Wolfram MathWorld. (n.d.). Linear Equations. Retrieved from https://mathworld.wolfram.com/LinearEquation.html