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The problem describes a line passing through two points \((-2,3)\) and \((4,-5)\). It then asks for the equation of the line after it is reflected horizontally.

Here’s the step-by-step solution:

### 1. Equation of the Original Line
We first need to find the equation of the line passing through the points \((-2, 3)\) and \((4, -5)\).

- The slope \(m\) is given by:
  \[
  m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 3}{4 - (-2)} = \frac{-8}{6} = -\frac{4}{3}
  \]

- Using the point-slope form of the equation of a line, \(y - y_1 = m(x - x_1)\), and using the point \((-2, 3)\):
  \[
  y - 3 = -\frac{4}{3}(x + 2)
  \]
  Simplifying this equation:
  \[
  y - 3 = -\frac{4}{3}x - \frac{8}{3}
  \]
  \[
  y = -\frac{4}{3}x - \frac{8}{3} + 3
  \]
  \[
  y = -\frac{4}{3}x + \frac{1}{3}
  \]
  
So, the equation of the original line is:
\[
y = -\frac{4}{3}x + \frac{1}{3}
\]

### 2. Horizontal Reflection
Reflecting the line horizontally means changing the sign of the \(y\)-coordinates of all points on the line. Mathematically, we replace \(y\) with \(-y\) in the equation.

So, the reflected line's equation is:
\[
-y = -\frac{4}{3}x + \frac{1}{3}
\]
Multiply through by \(-1\):
\[
y = \frac{4}{3}x - \frac{1}{3}
\]

### Final Answer:
The equation of the line after horizontal reflection is:
\[
y = \frac{4}{3}x - \frac{1}{3}
\]

Let me know if you'd like more details or have any questions.

### Related Questions:
1. How do you find the equation of a line passing through two points?
2. What is the geometric interpretation of reflecting a line horizontally?
3. How would the equation change if the line were reflected vertically instead?
4. How do you determine the slope of a line between two points?
5. Can a line's slope change after a reflection? If so, how?

### Tip:
When reflecting a line horizontally, remember that only the sign of the \(y\)-coordinates (or \(y\)-values) is affected, while the slope of the line may flip depending on the reflection.

Melalui dua titik (-2,3) dan (4,-5) dapat dibuat sebuah garis. Apabila garis itu direfleksikan horizontal maka persamaan garis hasil refleksinya adalah ...

Find the equation of a line passing through the points (-2, 3) and (4, -5), and learn how to reflect the line horizontally. This problem involves concepts of coordinate geometry, slope, and line reflection. Suitable for students in Grades 9-11.

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