Find The Line Parallel To Y = 9 X − 4 Y = 9x - 4 Y = 9 X − 4 That Includes The Point ( 2 , 7 (2, 7 ( 2 , 7 ].Enter The Value That Belongs In The Green Box: Y − [ ? ] = □ ( X − □ Y - [?] = \square(x - \square Y − [ ?] = □ ( X − □ ]Remember: Y − Y 1 = M ( X − X 1 Y - Y_1 = M(x - X_1 Y − Y 1 ​ = M ( X − X 1 ​ ]

Introduction

In mathematics, finding a line parallel to a given line is a fundamental concept in geometry and algebra. A parallel line is a line that lies in the same plane as the given line and never intersects it, no matter how far they are extended. In this article, we will explore how to find a line parallel to a given line that passes through a specific point.

Understanding the Problem

The problem requires us to find a line parallel to the line $y = 9x - 4$ that passes through the point $(2, 7)$. To solve this problem, we need to understand the concept of parallel lines and the equation of a line in slope-intercept form.

The Equation of a Line

The equation of a line in slope-intercept form is given by $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. In this case, the given line is $y = 9x - 4$, which means that the slope of the line is $9$ and the y-intercept is $-4$.

Finding a Parallel Line

To find a line parallel to the given line, we need to find a line with the same slope as the given line. Since the slope of the given line is $9$, the slope of the parallel line will also be $9$. The equation of the parallel line will be of the form $y = 9x + b$, where $b$ is the y-intercept of the parallel line.

Using the Point-Slope Form

The point-slope form of a line is given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line. We can use this form to find the equation of the parallel line that passes through the point $(2, 7)$.

Solving for the Y-Intercept

Using the point-slope form, we can substitute the values of $m$, $x_1$, and $y_1$ to get:

$y - 7 = 9(x - 2)$

Expanding the right-hand side of the equation, we get:

$y - 7 = 9x - 18$

Adding $7$ to both sides of the equation, we get:

$y = 9x - 11$

Conclusion

In conclusion, we have found the equation of a line parallel to the given line $y = 9x - 4$ that passes through the point $(2, 7)$. The equation of the parallel line is $y = 9x - 11$. This demonstrates the concept of finding a line parallel to a given line that passes through a specific point.

The Final Answer

The final answer is: $\boxed{11}$

Introduction

In our previous article, we explored how to find a line parallel to a given line that passes through a specific point. In this article, we will provide a Q&A guide to help you understand the concept of finding a parallel line and how to apply it in different scenarios.

Q: What is a parallel line?

A: A parallel line is a line that lies in the same plane as the given line and never intersects it, no matter how far they are extended.

Q: How do I find a line parallel to a given line?

A: To find a line parallel to a given line, you need to find a line with the same slope as the given line. The equation of the parallel line will be of the form $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.

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

A: The point-slope form of a line is given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.

Q: How do I use the point-slope form to find a parallel line?

A: To use the point-slope form to find a parallel line, you need to substitute the values of $m$, $x_1$, and $y_1$ into the equation. Then, you can solve for the y-intercept $b$ to get the equation of the parallel line.

Q: What if I don't have a point on the line? Can I still find a parallel line?

A: Yes, you can still find a parallel line even if you don't have a point on the line. You can use the slope of the given line to find the equation of the parallel line, and then use the point-slope form to find the y-intercept.

Q: How do I know if two lines are parallel?

A: Two lines are parallel if they have the same slope and never intersect each other, no matter how far they are extended.

Q: Can I find a parallel line if the given line is vertical?

A: No, you cannot find a parallel line if the given line is vertical. A vertical line has an undefined slope, and therefore, it is not possible to find a parallel line.

Q: Can I find a parallel line if the given line is horizontal?

A: Yes, you can find a parallel line if the given line is horizontal. A horizontal line has a slope of $0$, and therefore, you can find a parallel line with the same slope.

Conclusion

In conclusion, finding a parallel line is a fundamental concept in geometry and algebra. By understanding the concept of parallel lines and how to apply it in different scenarios, you can solve a wide range of problems in mathematics and science.

Frequently Asked Questions

• Q: What is the equation of a parallel line? A: The equation of a parallel line is of the form $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.
• Q: How do I find the y-intercept of a parallel line? A: To find the y-intercept of a parallel line, you need to use the point-slope form and substitute the values of $m$, $x_1$, and $y_1$ into the equation.
• Q: Can I find a parallel line if the given line is a circle? A: No, you cannot find a parallel line if the given line is a circle. A circle is a curved line, and therefore, it is not possible to find a parallel line.

Additional Resources

• Online Calculators: There are many online calculators available that can help you find a parallel line. You can search for "parallel line calculator" or "slope calculator" to find one.
• Math Books: There are many math books available that can help you learn more about finding parallel lines. You can search for "math books" or "geometry books" to find one.
• Online Courses: There are many online courses available that can help you learn more about finding parallel lines. You can search for "online math courses" or "geometry courses" to find one.