Line A Passes Through The Point { (-2,5)$}$ And Is Parallel To The Line Given By { Y = 3x + 9$}$.What Is The Equation Of Line A?Give Your Answer In The Form { Y = Mx + C$}$, Where { M$}$ And { C$}$ Are

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 point ${(-2,5)}$ and the line ${y = 3x + 9}$ to find the equation of line A.

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 have the same value of ${m}$ in the equation ${y = mx + c}$, then they are parallel.

Finding the Slope of Line A

Since line A is parallel to the line ${y = 3x + 9}$, it must have the same slope, which is ${3}$. Therefore, the equation of line A can be written as ${y = 3x + c}$, where ${c}$ is the y-intercept.

Finding the Y-Intercept of Line A

To find the y-intercept of line A, we can use the given point ${(-2,5)}$ and substitute it into the equation ${y = 3x + c}$. This gives us:

${5 = 3(-2) + c}$

Simplifying the equation, we get:

${5 = -6 + c}$

Adding ${6}$ to both sides, we get:

${c = 11}$

Therefore, the equation of line A is ${y = 3x + 11}$.

Conclusion

In this article, we have seen how to find the equation of a line that passes through a given point and is parallel to another line. We used the given point ${(-2,5)}$ and the line ${y = 3x + 9}$ to find the equation of line A, which is ${y = 3x + 11}$. This demonstrates the concept of parallel lines and how to find the equation of a line that is parallel to another line.

Example

Find the equation of the line that passes through the point ${(3,7)}$ and is parallel to the line ${y = 2x - 4}$.

Solution

Since the line is parallel to ${y = 2x - 4}$, it must have the same slope, which is ${2}$. Therefore, the equation of the line can be written as ${y = 2x + c}$, where ${c}$ is the y-intercept.

To find the y-intercept, we can use the given point ${(3,7)}$ and substitute it into the equation ${y = 2x + c}$. This gives us:

${7 = 2(3) + c}$

Simplifying the equation, we get:

${7 = 6 + c}$

Subtracting ${6}$ from both sides, we get:

${c = 1}$

Therefore, the equation of the line is ${y = 2x + 1}$.

Tips and Tricks

• When finding the equation of a line that is parallel to another line, make sure to use the same slope.
• When finding the y-intercept of a line, use the given point and substitute it into the equation.
• Simplify the equation by combining like terms.

Frequently Asked Questions

• What is the equation of a line that passes through the point ${(4,9)}$ and is parallel to the line ${y = 5x - 2}$?
  • The equation of the line is ${y = 5x + 1}$.
• What is the equation of a line that passes through the point ${(2,6)}$ and is parallel to the line ${y = 3x + 1}$?
  • The equation of the line is ${y = 3x + 4}$.

Conclusion

$$$$$$

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. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the equation of a line that passes through the point (4,9) and is parallel to the line y = 5x - 2?

A: The equation of the line is y = 5x + 1.

Explanation: Since the line is parallel to y = 5x - 2, it must have the same slope, which is 5. Therefore, the equation of the line can be written as y = 5x + c, where c is the y-intercept. To find the y-intercept, we can use the given point (4,9) and substitute it into the equation y = 5x + c. This gives us:

9 = 5(4) + c

Simplifying the equation, we get:

9 = 20 + c

Subtracting 20 from both sides, we get:

c = -11

Therefore, the equation of the line is y = 5x - 11.

Q: What is the equation of a line that passes through the point (2,6) and is parallel to the line y = 3x + 1?

A: The equation of the line is y = 3x + 4.

Explanation: Since the line is parallel to y = 3x + 1, it must have the same slope, which is 3. Therefore, the equation of the line can be written as y = 3x + c, where c is the y-intercept. To find the y-intercept, we can use the given point (2,6) and substitute it into the equation y = 3x + c. This gives us:

6 = 3(2) + c

Simplifying the equation, we get:

6 = 6 + c

Subtracting 6 from both sides, we get:

c = 0

Therefore, the equation of the line is y = 3x.

Q: What is the equation of a line that passes through the point (1,3) and is parallel to the line y = 2x - 4?

A: The equation of the line is y = 2x + 1.

Explanation: Since the line is parallel to y = 2x - 4, it must have the same slope, which is 2. Therefore, the equation of the line can be written as y = 2x + c, where c is the y-intercept. To find the y-intercept, we can use the given point (1,3) and substitute it into the equation y = 2x + c. This gives us:

3 = 2(1) + c

Simplifying the equation, we get:

3 = 2 + c

Subtracting 2 from both sides, we get:

c = 1

Therefore, the equation of the line is y = 2x + 1.

Q: What is the equation of a line that passes through the point (3,7) and is parallel to the line y = 4x - 2?

A: The equation of the line is y = 4x + 3.

Explanation: Since the line is parallel to y = 4x - 2, it must have the same slope, which is 4. Therefore, the equation of the line can be written as y = 4x + c, where c is the y-intercept. To find the y-intercept, we can use the given point (3,7) and substitute it into the equation y = 4x + c. This gives us:

7 = 4(3) + c

Simplifying the equation, we get:

7 = 12 + c

Subtracting 12 from both sides, we get:

c = -5

Therefore, the equation of the line is y = 4x - 5.

Conclusion

In this article, we have answered some frequently asked questions related to finding the equation of a line that is parallel to another line. We have seen how to use the given point and the slope of the line to find the equation of the line. We hope that this article has been helpful in understanding this concept.