Which Equation Has A Graph That Passes Through The Origin And Has A Slope Of 0?A. $x = 0$B. $x + Y = 0$C. $y = X$D. $y = 0$

Introduction

Linear equations are a fundamental concept in mathematics, and understanding their graphs is crucial for various applications in science, engineering, and other fields. In this article, we will explore which equation has a graph that passes through the origin and has a slope of 0.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form of:

y = mx + b

where:

• y is the dependent variable
• x is the independent variable
• m is the slope of the line
• b is the y-intercept

What is the Slope of a Line?

The slope of a line is a measure of how steep it is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run). A slope of 0 means that the line is horizontal and does not change in the vertical direction.

What is the Origin?

The origin is the point where the x-axis and y-axis intersect. It is represented by the coordinates (0, 0).

Which Equation Passes Through the Origin and Has a Slope of 0?

To determine which equation passes through the origin and has a slope of 0, we need to analyze each option.

Option A: $x = 0$

This equation represents a vertical line that passes through the y-axis at x = 0. It does not have a slope of 0, as it is a vertical line.

Option B: $x + y = 0$

This equation can be rewritten as:

y = -x

This equation represents a line with a slope of -1. It does not pass through the origin, as the point (0, 0) does not satisfy the equation.

Option C: $y = x$

This equation represents a line with a slope of 1. It does not pass through the origin, as the point (0, 0) does not satisfy the equation.

Option D: $y = 0$

This equation represents a horizontal line that passes through the x-axis at y = 0. It has a slope of 0, as it does not change in the vertical direction.

Conclusion

Based on the analysis, the equation that passes through the origin and has a slope of 0 is:

y = 0

This equation represents a horizontal line that passes through the x-axis at y = 0. It has a slope of 0, as it does not change in the vertical direction.

Key Takeaways

• A linear equation is an equation in which the highest power of the variable(s) is 1.
• The slope of a line is a measure of how steep it is.
• The origin is the point where the x-axis and y-axis intersect.
• The equation $y = 0$ passes through the origin and has a slope of 0.

Further Reading

For more information on linear equations and their graphs, we recommend the following resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram MathWorld: Linear Equations

References

• [1] Khan Academy. (n.d.). Linear Equations. Retrieved from <https://www.khanacademy.org/math/algebra/x2f1f4f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f1f
  Frequently Asked Questions (FAQs) =====================================

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form of:

y = mx + b

where:

• y is the dependent variable
• x is the independent variable
• m is the slope of the line
• b is the y-intercept

Q: What is the slope of a line?

A: The slope of a line is a measure of how steep it is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run). A slope of 0 means that the line is horizontal and does not change in the vertical direction.

Q: What is the origin?

A: The origin is the point where the x-axis and y-axis intersect. It is represented by the coordinates (0, 0).

Q: Which equation passes through the origin and has a slope of 0?

A: The equation that passes through the origin and has a slope of 0 is:

y = 0

This equation represents a horizontal line that passes through the x-axis at y = 0. It has a slope of 0, as it does not change in the vertical direction.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. A quadratic equation is an equation in which the highest power of the variable(s) is 2. For example:

• Linear equation: y = 2x + 3
• Quadratic equation: y = x^2 + 2x + 1

Q: How do I graph a linear equation?

A: To graph a linear equation, you can use the following steps:

1. Identify the slope (m) and y-intercept (b) of the equation.
2. Plot the y-intercept (b) on the y-axis.
3. Use the slope (m) to determine the direction and steepness of the line.
4. Plot additional points on the line using the slope and y-intercept.
5. Draw a line through the points to create the graph.

Q: What is the equation of a line that passes through the points (2, 3) and (4, 5)?

A: To find the equation of a line that passes through two points, you can use the following steps:

1. Calculate the slope (m) using the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points.

2. Use the slope (m) and one of the points to find the y-intercept (b) using the equation:

y = mx + b

3. Simplify the equation to find the final form of the equation.

For the points (2, 3) and (4, 5), the slope (m) is:

m = (5 - 3) / (4 - 2) = 1

Using the slope (m) and the point (2, 3), the equation of the line is:

y = x + 1

Q: How do I find the equation of a line that passes through the origin?

A: To find the equation of a line that passes through the origin, you can use the following steps:

1. Identify the slope (m) of the line.
2. Use the slope (m) and the point (0, 0) to find the y-intercept (b) using the equation:

y = mx + b

3. Simplify the equation to find the final form of the equation.

For example, if the slope (m) is 2, the equation of the line is:

y = 2x

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

A: To find the equation of a line that has a slope of 3 and passes through the point (1, 2), you can use the following steps:

1. Use the slope (m) and the point (1, 2) to find the y-intercept (b) using the equation:

y = mx + b

2. Simplify the equation to find the final form of the equation.

For the slope (m) of 3 and the point (1, 2), the equation of the line is:

y = 3x - 1

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

A: To find the equation of a line that passes through two points, you can use the following steps:

1. Calculate the slope (m) using the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points.

2. Use the slope (m) and one of the points to find the y-intercept (b) using the equation:

y = mx + b

3. Simplify the equation to find the final form of the equation.

For example, if the points are (2, 3) and (4, 5), the slope (m) is:

m = (5 - 3) / (4 - 2) = 1

Using the slope (m) and the point (2, 3), the equation of the line is:

y = x + 1

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

A: To find the equation of a line that has a slope of -2 and passes through the point (3, 4), you can use the following steps:

1. Use the slope (m) and the point (3, 4) to find the y-intercept (b) using the equation:

y = mx + b

2. Simplify the equation to find the final form of the equation.

For the slope (m) of -2 and the point (3, 4), the equation of the line is:

y = -2x + 10

Q: How do I find the equation of a line that passes through the origin and has a slope of 4?

A: To find the equation of a line that passes through the origin and has a slope of 4, you can use the following steps:

1. Use the slope (m) and the point (0, 0) to find the y-intercept (b) using the equation:

y = mx + b

2. Simplify the equation to find the final form of the equation.

For the slope (m) of 4 and the point (0, 0), the equation of the line is:

y = 4x