Find the equation of the line using the given information. Passes through these two points: \( (x, y)=(6,4), \quad(x, y)=(6,9) \)

To find the equation of the line that passes through the points \( (6, 4) \) and \( (6, 9) \), we first notice that both points have the same x-coordinate (6). This means the line is vertical. The equation of a vertical line is simply \( x = a \), where \( a \) is the constant x-value. Since both points share an x-value of 6, the equation of the line is: \[ x = 6 \] This means that for any y-value, the line will always be located at x = 6. Also, vertical lines have an undefined slope, which can be an interesting concept to explore. Typically, a slope is calculated as \( \frac{y_2 - y_1}{x_2 - x_1} \). Here, with \( x_2 - x_1 = 0 \), we run into division by zero, which mathematically confirms the undefined slope characteristic of vertical lines!