Final answer:
The equation for the vertical line passing through the point (1, 9) is x = 1, and the equation for the horizontal line is y = 9. These equations represent lines that are perpendicular to each other, with the vertical line maintaining a constant x-coordinate and the horizontal line maintaining a constant y-coordinate.
Step-by-step explanation:
To write equations for the vertical and horizontal lines passing through the point (1, 9), we need to understand that a vertical line has an undefined slope and a horizontal line has a slope of zero. Since these lines are defined solely by their x- or y-coordinate values in this situation, the equations are straightforward.
Equation of a Vertical Line
For a vertical line that passes through the point (1, 9), the x-coordinate remains constant. Therefore, the equation is x = 1.
Equation of a Horizontal Line
For a horizontal line that passes through the point (1, 9), the y-coordinate remains constant. Hence, the equation is y = 9.
It is important to note that these lines are perpendicular to each other and will not change no matter what other points are on the lines, as they are defined strictly by their x and y values at (1, 9) respectively.