https://file.aiquickdraw.com/mathbot/file/1725076724919cwiz8teg.jpg

Cari persamaan garis lurus yang selari dengan garis lurus yang diberi

To find the equation of a line that is parallel to the given line, we need to understand the properties of parallel lines in a coordinate plane. 

### Step-by-Step Solution:

1. **Identify the Slope of the Given Line**:
   The given line is \( y = 3x - 2 \). This is in slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept. Here, the slope \( m \) is 3.

2. **Understand Parallel Line Properties**:
   Lines that are parallel to each other have the same slope. Therefore, any line parallel to \( y = 3x - 2 \) will also have a slope of 3.

3. **Determine the Equation of the Parallel Line**:
   Since the new line must be parallel, it must have the form \( y = 3x + c \), where \( c \) is the y-intercept of the new line.

4. **Use the Point Given to Find the Y-Intercept**:
   The problem gives a point through which the parallel line passes, specifically the point \((-4, 2)\). We substitute these coordinates into the equation \( y = 3x + c \) to solve for \( c \):
   
   \[
   2 = 3(-4) + c
   \]
   
   \[
   2 = -12 + c
   \]
   
   \[
   c = 14
   \]

5. **Write the Final Equation**:
   The equation of the line parallel to \( y = 3x - 2 \) and passing through \((-4, 2)\) is:

   \[
   y = 3x + 14
   \]

### Conclusion:
The equation of the line parallel to the given line and passing through the point \((-4, 2)\) is \( y = 3x + 14 \).

Would you like more details or have any questions about this solution?

Here are 5 additional questions that you might find helpful:

1. How do you find the slope of a line from two given points?
2. What is the general form of a line equation and how is it different from the slope-intercept form?
3. How do you determine if two lines are perpendicular?
4. What is the distance between two parallel lines?
5. How can you find the point of intersection between two lines?

**Tip:** When working with line equations, always check if you need the slope-intercept form or another form, like point-slope form, to make your calculations easier.

Learn how to find the equation of a line parallel to y = 3x - 2 and passing through the point (-4, 2) using slope-intercept form. This problem covers concepts of lines, slopes, and coordinate geometry, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation