What Is The Equation Of The Line Parallel To $3x + 5y = 11$ That Passes Through The Point $(15, 4$\]?A. $y = \frac{5}{3}x - 29$ B. $y = \frac{5}{3}x - 21$ C. $y = -\frac{3}{5}x + 5$ D. $y =

$$$$

Introduction

In mathematics, the concept of parallel lines is a fundamental idea in geometry and algebra. Two lines are said to be parallel if they lie in the same plane and never intersect, no matter how far they are extended. In this article, we will explore the equation of a line that is parallel to a given line and passes through a specific point.

Understanding the Given Line

The given line is represented by the equation $3x + 5y = 11$. To find the equation of a line parallel to this line, we need to understand the slope of the given line. The slope-intercept form of a line is given by $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

To convert the given equation to slope-intercept form, we can solve for $y$:

$$3x + 5y = 11$$

$$5y = -3x + 11$$

$$y = -\frac{3}{5}x + \frac{11}{5}$$

From this equation, we can see that the slope of the given line is $-\frac{3}{5}$.

Finding the Equation of the Parallel Line

Since the line we are looking for is parallel to the given line, it must have the same slope. Therefore, the equation of the parallel line will also have a slope of $-\frac{3}{5}$.

However, we are given a point $(15, 4)$ that the parallel line must pass through. To find the equation of the parallel line, we can use the point-slope form of a line, which is given by:

$$y - y_1 = m(x - x_1)$$

where $(x_1, y_1)$ is the given point and $m$ is the slope.

Plugging in the values, we get:

$$y - 4 = -\frac{3}{5}(x - 15)$$

To simplify this equation, we can multiply both sides by 5 to eliminate the fraction:

$$5(y - 4) = -3(x - 15)$$

Expanding the left-hand side, we get:

$$5y - 20 = -3x + 45$$

Adding 20 to both sides, we get:

$$5y = -3x + 65$$

Dividing both sides by 5, we get:

$$y = -\frac{3}{5}x + \frac{65}{5}$$

Simplifying further, we get:

$$y = -\frac{3}{5}x + 13$$

Comparing with the Answer Choices

Now that we have found the equation of the parallel line, we can compare it with the answer choices:

A. $y = \frac{5}{3}x - 29$ B. $y = \frac{5}{3}x - 21$ C. $y = -\frac{3}{5}x + 5$ D. $y = -\frac{3}{5}x + 13$

From the equation we derived, we can see that the correct answer is:

D. $y = -\frac{3}{5}x + 13$

Conclusion

In this article, we explored the concept of parallel lines and how to find the equation of a line that is parallel to a given line and passes through a specific point. We used the point-slope form of a line to derive the equation of the parallel line and compared it with the answer choices. The correct answer is D. $y = -\frac{3}{5}x + 13$.

Frequently Asked Questions

• What is the slope of the given line?
  • The slope of the given line is $-\frac{3}{5}$.
• How do we find the equation of a line that is parallel to a given line?
  • We can use the point-slope form of a line, which is given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point and $m$ is the slope.
• What is the equation of the parallel line that passes through the point $(15, 4)$?
  • The equation of the parallel line is $y = -\frac{3}{5}x + 13$.

Final Answer

The final answer is D. $y = -\frac{3}{5}x + 13$.

$$$$

Introduction

In our previous article, we explored the concept of parallel lines and how to find the equation of a line that is parallel to a given line and passes through a specific point. We used the point-slope form of a line to derive the equation of the parallel line and compared it with the answer choices. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q1: What is the slope of the given line?

A1: The slope of the given line is $-\frac{3}{5}$.

Q2: How do we find the equation of a line that is parallel to a given line?

A2: We can use the point-slope form of a line, which is given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point and $m$ is the slope.

Q3: What is the equation of the parallel line that passes through the point $(15, 4)$?

A3: The equation of the parallel line is $y = -\frac{3}{5}x + 13$.

Q4: How do we know that the line we are looking for is parallel to the given line?

A4: We know that the line we are looking for is parallel to the given line because it has the same slope as the given line.

Q5: Can we use the slope-intercept form of a line to find the equation of the parallel line?

A5: Yes, we can use the slope-intercept form of a line to find the equation of the parallel line. However, we need to make sure that the slope is the same as the slope of the given line.

Q6: What is the y-intercept of the parallel line?

A6: The y-intercept of the parallel line is 13.

Q7: How do we compare the equation of the parallel line with the answer choices?

A7: We compare the equation of the parallel line with the answer choices by plugging in the values of x and y into the equation and checking if it matches any of the answer choices.

Q8: What is the final answer?

A8: The final answer is D. $y = -\frac{3}{5}x + 13$.

Conclusion

In this article, we answered some frequently asked questions related to the topic of finding the equation of a line that is parallel to a given line and passes through a specific point. We hope that this article has been helpful in clarifying any doubts that you may have had.

Frequently Asked Questions

• What is the slope of the given line?
• How do we find the equation of a line that is parallel to a given line?
• What is the equation of the parallel line that passes through the point $(15, 4)$?
• How do we know that the line we are looking for is parallel to the given line?
• Can we use the slope-intercept form of a line to find the equation of the parallel line?
• What is the y-intercept of the parallel line?
• How do we compare the equation of the parallel line with the answer choices?
• What is the final answer?

Final Answer

The final answer is D. $y = -\frac{3}{5}x + 13$.