What is the equation of a line passing through the point (5, 2) parallel to y = -3x + 1?

To find the equation of a line passing through the point \((5, 2)\) and parallel to the line \(y = -3x + 1\), we start by noting that parallel lines have the same slope.

1. **Identify the slope of the given line:**

   The given line is \(y = -3x + 1\), which is in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

   - Here, the slope \(m\) is \(-3\).

2. **Use the point-slope form of the equation of a line:**

   The point-slope form 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. Substituting the point \((5, 2)\) and the slope \(-3\):

   \[
   y - 2 = -3(x - 5)
   \]

3. **Simplify the equation:**

   Distribute the slope and simplify:

   \[
   y - 2 = -3x + 15
   \]

   Add 2 to both sides to solve for \(y\):

   \[
   y = -3x + 17
   \]

Therefore, the equation of the line passing through the point \((5, 2)\) and parallel to the line \(y = -3x + 1\) is:

\[
\boxed{y = -3x + 17}
\]

Would you like further details or have any questions?

Here are some related questions for further practice:

1. What is the equation of a line passing through the point \((1, 4)\) parallel to the line \(y = 2x - 3\)?
2. How do you find the equation of a line perpendicular to \(y = \frac{1}{2}x + 6\) passing through the origin?
3. What is the slope of a line parallel to the line given by \(3x - 4y = 12\)?
4. Find the y-intercept of the line that passes through \((3, 7)\) and is parallel to \(y = -4x + 2\).
5. How do you determine if two lines are parallel or perpendicular by looking at their equations?

**Tip:** When finding equations of parallel lines, remember they always share the same slope.

Learn how to find the equation of a line passing through the point (5, 2) and parallel to the line y = -3x + 1. This problem involves using the point-slope form of a line and understanding parallel lines in geometry. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation