Answer:
x = 5
Step-by-step explanation:
If a line has an undefined slope, it means it is a vertical line. This is because the slope of a line is defined as the change in the y-coordinates divided by the change in the x-coordinates.
[tex]\textsf{Slope}\;(m)=\dfrac{\Delta y}{\Delta x}[/tex]
For a vertical line, the difference in x-coordinates (Δx) between any two points on the line is always zero, resulting in division by zero when calculating the slope, which means the slope is undefined.
The equation of a vertical line passing through the point (a, b) is given by x = a. In this case, the point is (5, -9), so the equation of the line is x = 5.
Therefore, the equation of the line in standard form with an undefined slope and passing through the point (5, -9) is:
[tex]\huge\boxed{\boxed{x=5}}[/tex]
