General Form of a Linear Equation

Oct 13, 2025 by windailys.com 45 views

Introduction

In mathematics, a linear equation is a type of equation that can be written in the form of a straight line. It is a fundamental concept in algebra and is used to represent a relationship between two variables, typically x and y. In this article, we will focus on writing the equation of a line with a given slope and y-intercept.

What is the Slope-Intercept Form?

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

y = mx + b

where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, while the y-intercept represents the point where the line intersects the y-axis.

Given Information

In this problem, we are given a line with a slope of 1 and a y-intercept of -1. We need to write the equation of this line in general form.

General Form of a Linear Equation

The general form of a linear equation is given by:

ax + by + c = 0

where a, b, and c are constants. To write the equation of a line in general form, we need to multiply the slope-intercept form by the coefficient of x and then rearrange the terms.

Step 1: Multiply the Slope-Intercept Form

We start by multiplying the slope-intercept form by the coefficient of x, which is 1 in this case.

y = x - 1

Step 2: Rearrange the Terms

Next, we need to rearrange the terms to get the general form of the equation.

-x + y = -1

Step 3: Write the Equation in General Form

Now, we can write the equation in general form by multiplying both sides of the equation by -1.

-x + y + 1 = 0

Conclusion

In this article, we have learned how to write the equation of a line with a given slope and y-intercept. We have used the slope-intercept form and the general form of a linear equation to derive the equation of the line. The final answer is:

The Correct Answer is A. -x+y+1=0

Additional Examples

Here are some additional examples of writing the equation of a line with a given slope and y-intercept.

A line with a slope of 2 and a y-intercept of 3: y = 2x + 3 => 2x - y + 3 = 0
A line with a slope of -1 and a y-intercept of 2: y = -x + 2 => x + y - 2 = 0
A line with a slope of 0 and a y-intercept of 1: y = 1 => x + y - 1 = 0

Tips and Tricks

When writing the equation of a line, make sure to multiply the slope-intercept form by the coefficient of x.
When rearranging the terms, make sure to keep the same order of operations.
When writing the equation in general form, make sure to multiply both sides of the equation by the correct coefficient.

Conclusion

Introduction

In our previous article, we learned how to write the equation of a line with a given slope and y-intercept. In this article, we will answer some frequently asked questions about writing the equation of a line.

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

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

y = mx + b

where m is the slope of the line and b is the y-intercept.

Q: What is the general form of a linear equation?

A: The general form of a linear equation is given by:

ax + by + c = 0

where a, b, and c are constants.

Q: How do I write the equation of a line in general form?

A: To write the equation of a line in general form, you need to multiply the slope-intercept form by the coefficient of x and then rearrange the terms.

Q: What is the coefficient of x?

A: The coefficient of x is the number that is multiplied by x in the slope-intercept form.

Q: How do I multiply the slope-intercept form by the coefficient of x?

A: To multiply the slope-intercept form by the coefficient of x, you need to multiply both sides of the equation by the coefficient of x.

Q: What is the y-intercept?

A: The y-intercept is the point where the line intersects the y-axis.

Q: How do I find the y-intercept?

A: To find the y-intercept, you need to set x equal to 0 in the slope-intercept form.

Q: What is the slope?

A: The slope is the rate of change of the line.

Q: How do I find the slope?

A: To find the slope, you need to divide the change in y by the change in x.

Q: What is the equation of a line with a slope of 1 and a y-intercept of -1?

A: The equation of a line with a slope of 1 and a y-intercept of -1 is:

-x + y + 1 = 0

Q: What is the equation of a line with a slope of 2 and a y-intercept of 3?

A: The equation of a line with a slope of 2 and a y-intercept of 3 is:

2x - y + 3 = 0

Q: What is the equation of a line with a slope of -1 and a y-intercept of 2?

A: The equation of a line with a slope of -1 and a y-intercept of 2 is:

x + y - 2 = 0

Q: What is the equation of a line with a slope of 0 and a y-intercept of 1?

A: The equation of a line with a slope of 0 and a y-intercept of 1 is:

x + y - 1 = 0

Conclusion

In conclusion, writing the equation of a line with a given slope and y-intercept is a straightforward process that involves using the slope-intercept form and the general form of a linear equation. By following the steps outlined in this article, you can write the equation of a line with ease.

Additional Resources

Tips and Tricks

When writing the equation of a line, make sure to multiply the slope-intercept form by the coefficient of x.
When rearranging the terms, make sure to keep the same order of operations.
When writing the equation in general form, make sure to multiply both sides of the equation by the correct coefficient.

Conclusion

In conclusion, writing the equation of a line with a given slope and y-intercept is a fundamental concept in algebra. By following the steps outlined in this article, you can write the equation of a line with ease.