https://file.aiquickdraw.com/mathbot/file/1725968091408p4g9qv1w.jpg

The problem you are asking about is as follows:

**Question 20**: 
- The equation of the line \( y = x + 3 \) is reflected over the y-axis. What is the equation of the reflection?

To solve this, we need to know how a reflection over the y-axis affects the equation of a line. The general rule is that reflecting a point \((x, y)\) over the y-axis transforms it into \((-x, y)\). For lines, this means we change the sign of the \(x\)-terms in the equation.

Starting with the given equation:
\[
y = x + 3
\]
Reflecting over the y-axis, we substitute \( x \) with \( -x \):
\[
y = -x + 3
\]
Rewriting this in the form of options given in the problem (with all variables on one side):
\[
x + y = 3
\]

Thus, the correct answer is **option a: \( x + y = 3 \)**.

---

Would you like more details on this, or do you have any other questions?

Here are five related questions to deepen your understanding:
1. How does reflecting a line over the x-axis affect its equation?
2. What happens if we reflect a line over the origin?
3. Can you reflect any line over the y-axis and still have a line with the same slope?
4. How can you determine the slope of a line from its equation in standard form?
5. What is the geometric significance of reflecting a line over the y-axis?

**Tip**: When reflecting an equation, always focus on how each point on the line shifts to its new location based on the axis of reflection.

Persamaan garis y = x + 3 dicerminkan terhadap sumbu Y. Persamaan bayangannya adalah?

Learn how to find the reflection of the line y = x + 3 over the y-axis. This problem covers key algebraic and geometric concepts, including reflection in coordinate geometry. Suitable for 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