Let's find the equation of the line passing through the points [tex]\((-25, 50)\)[/tex] and [tex]\((25, 50)\)[/tex] in slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
### 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]
