https://file.aiquickdraw.com/mathbot/file/1726174961289v4l39x6l.jpg

The problem asks to find the equation of a line that is parallel to the line \( y = \frac{2}{3}x - 3 \) and passes through the point \((-3, 1)\).

### Step 1: Identify the slope of the given line.
The given line is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope. From the equation \( y = \frac{2}{3}x - 3 \), the slope \( m = \frac{2}{3} \).

Since parallel lines have the same slope, the slope of the new line will also be \( m = \frac{2}{3} \).

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

We know the slope \( m = \frac{2}{3} \) and the line passes through the point \( (-3, 1) \). Substituting these values into the point-slope form:

\[
y - 1 = \frac{2}{3}(x + 3)
\]

### Step 3: Simplify the equation.
Distribute the slope \( \frac{2}{3} \):

\[
y - 1 = \frac{2}{3}x + 2
\]

Now, add 1 to both sides to isolate \( y \):

\[
y = \frac{2}{3}x + 3
\]

### Final Equation:
The equation of the line parallel to \( y = \frac{2}{3}x - 3 \) and passing through the point \( (-3, 1) \) is:
\[
y = \frac{2}{3}x + 3
\]

---

Would you like more details or further clarification on this? Here are some related questions:

1. How do you find the slope of a line from its equation?
2. What is the difference between the point-slope form and the slope-intercept form of a line?
3. How can you find the equation of a line perpendicular to another line?
4. What is the geometric interpretation of parallel and perpendicular lines?
5. How do you graph a line using its slope and a point?

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

Write the equation of a line that is parallel to y = 2/3x - 3 and passes through the point (-3, 1).

Learn how to find the equation of a line parallel to y = 2/3x - 3 that passes through the point (-3, 1) using the point-slope form. This step-by-step guide simplifies linear equations and the concept of parallel lines for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation