Line { G $}$ Passes Through The Point { (8,11)$}$ And Is Parallel To The Line Given By { Y = 6(2x + 3) $}$.What Is The Equation Of Line { G $}$?Give Your Answer In The Form { Y = Mx + C $}$, Where

Mar 9, 2025 by ADMIN 197 views

**Solving for the Equation of Line G**

Introduction

In this article, we will explore the concept of parallel lines and how to find the equation of a line that passes through a given point and is parallel to another line. We will use the given information to find the equation of line G in the form y = mx + c.

Understanding Parallel Lines

Two lines are said to be parallel if they have the same slope but different y-intercepts. In other words, if two lines are parallel, they will never intersect, and their slopes will be equal.

Finding the Slope of Line G

To find the equation of line G, we need to find its slope. Since line G is parallel to the line given by y = 6(2x + 3), we can find the slope of this line and use it as the slope of line G.

The given line can be rewritten as y = 12x + 18. The slope of this line is 12, which means that the slope of line G is also 12.

Using the Point-Slope Form

Now that we have the slope of line G, we can use the point-slope form to find its equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

We are given that line G passes through the point (8, 11). We can substitute this point and the slope of line G into the point-slope form to get:

y - 11 = 12(x - 8)

Simplifying the Equation

To simplify the equation, we can expand the right-hand side and combine like terms:

y - 11 = 12x - 96

Now, we can add 11 to both sides to get:

y = 12x - 85

Conclusion

In this article, we found the equation of line G in the form y = mx + c. We used the given information to find the slope of line G and then used the point-slope form to find its equation. The final equation of line G is y = 12x - 85.

Key Takeaways

Two lines are parallel if they have the same slope but different y-intercepts.
The slope of a line can be found using the point-slope form.
The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Additional Resources

For more information on parallel lines and the point-slope form, please see the following resources:

Frequently Asked Questions

Q: What is the equation of line G? A: The equation of line G is y = 12x - 85.
Q: How do I find the slope of a line? A: You can find the slope of a line using the point-slope form.
Q: What is the point-slope form? A: The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Solving for the Equation of Line G: Q&A =============================================

Introduction

In our previous article, we explored the concept of parallel lines and how to find the equation of a line that passes through a given point and is parallel to another line. We used the given information to find the equation of line G in the form y = mx + c. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is the equation of line G?

A: The equation of line G is y = 12x - 85.

Q: How do I find the slope of a line?

A: You can find the slope of a line using the point-slope form. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Q: What is the point-slope form?

A: The point-slope form is a way to write the equation of a line using the slope and a point on the line. It is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Q: How do I find the equation of a line that passes through a given point and is parallel to another line?

A: To find the equation of a line that passes through a given point and is parallel to another line, you need to find the slope of the given line and use it as the slope of the new line. Then, you can use the point-slope form to find the equation of the new line.

Q: What is the difference between the slope and the y-intercept of a line?

A: The slope of a line is a measure of how steep the line is, while the y-intercept is the point where the line intersects the y-axis. The slope is a measure of the rate of change of the line, while the y-intercept is a measure of the starting point of the line.

Q: How do I graph a line using its equation?

A: To graph a line using its equation, you can use the slope-intercept form (y = mx + c) or the point-slope form (y - y1 = m(x - x1)). You can also use a graphing calculator or a graphing software to graph the line.

Q: What is the significance of the slope of a line?

A: The slope of a line is a measure of how steep the line is, and it can be used to determine the rate of change of the line. A line with a positive slope is increasing, while a line with a negative slope is decreasing.

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 two-point form. The two-point form is given by y - y1 = m(x - x1), where (x1, y1) and (x2, y2) are the two points on the line.

Q: What is the difference between the slope and the y-intercept of a line in the context of parallel lines?

A: In the context of parallel lines, the slope of the two lines is the same, but the y-intercept is different. This means that the two lines have the same steepness, but they start at different points on the y-axis.