Solving for a Variable with Given Coordinates
To solve for \( n \), we need to use the given information about the coordinates of the points on the line. The coordinates of the two points are given as \( P_1(-18, 18) \) and \( P_2(2, n) \).
The slope \( m \) of a line passing through two points \( P_1(x_1, y_1) \) and \( P_2(x_2, y_2) \) can be found using the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Given that the slope is 0 (from the information provided about the equation of the line), this means that the line is horizontal and there is no change in the y-values between points \( P_1 \) and \( P_2 \). Therefore, \( y_1 = y_2 \), or equivalently, \( 18 = n \).
So, the value of \( n \) is 18.
