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## Sagot :

### Step 1: Determine the slope (m)

The formula to calculate the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

For our points, [tex]\((x_1, y_1) = (-25, 50)\)[/tex] and [tex]\((x_2, y_2) = (25, 50)\)[/tex]:

[tex]\[ m = \frac{50 - 50}{25 - (-25)} = \frac{0}{50} = 0 \][/tex]

### Step 2: Insert the slope and one of the points into the slope-intercept form

Given that the slope [tex]\(m\)[/tex] is 0, the equation of the line simplifies to:

[tex]\[ y = 0 * x + b \implies y = b \][/tex]

### Step 3: Find the y-intercept (b)

Using either of the points to find [tex]\(b\)[/tex]. Let's use [tex]\((x_1, y_1) = (-25, 50)\)[/tex]:

[tex]\[ y = 50 \implies 50 = b \implies b = 50 \][/tex]

### Conclusion

Thus, the equation of the line is:

[tex]\[ y = 50 \][/tex]

So the correct answer is:

[tex]\[ y = 50 \][/tex]