https://file.aiquickdraw.com/mathbot/file/17308306809033al3ah71.jpg

To find the equation of line \( B \) which passes through point \( P \) and is parallel to line \( A \), let's analyze the steps needed to solve this:

1. **Identify the slope of line \( A \)**: Since line \( B \) is parallel to line \( A \), it will have the same slope as line \( A \). We can determine the slope by choosing two points on line \( A \) from the graph and calculating the slope \( m \) using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]

2. **Equation of line \( A \)**: By identifying points along line \( A \), we can find its slope. From the graph, let's choose two points on line \( A \) to determine this slope.

3. **Point \( P \)**: Note the coordinates of point \( P \) (let's call them \( (x_1, y_1) \)), which will serve as a reference point for line \( B \).

4. **Formulate the equation of line \( B \)**: Using the point-slope form of a line \( y - y_1 = m(x - x_1) \), substitute the slope \( m \) (same as line \( A \)) and the coordinates of point \( P \).

5. **Convert to slope-intercept form \( y = mx + c \)**: Simplify the equation to get it in the form \( y = mx + c \).

Let’s go through these steps with the values from the graph:

1. Identify the coordinates of two points on line \( A \) to find its slope.
2. Identify the coordinates of point \( P \).
3. Substitute values into the point-slope form.

Once you try these steps, let me know if you want further assistance or if I should solve it with specific values from the graph. 

---

Would you like a more detailed solution with specific values?

Here are 5 additional questions to expand your understanding:
1. How can you determine if two lines are parallel based on their slopes?
2. What happens to the equation of a line if it shifts vertically but remains parallel to its original?
3. How does changing the slope affect the steepness of the line?
4. Why is the point-slope form useful for finding the equation of a line through a given point?
5. How can you verify if a point lies on a specific line by using its equation?

**Tip:** When two lines are parallel, they always have the same slope but different \( y \)-intercepts (unless they are the same line).

If line B is drawn such that it passes through point P and is parallel to line A, what is the equation of line B?

Learn how to find the equation of a line that is parallel to a given line and passes through a specific point. This solution covers concepts of linear equations, slope calculations, and parallel line properties. Suitable for high school students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation