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.