Question

1. write equation of the vertical line that passes through the point (3,5)

type a response
hints

1. m = _______

axis: _______
intercept: ____
equation: _______

Explanation:

Step1: Recall vertical line properties

A vertical line has an undefined slope (since the change in x is 0, and slope \( m=\frac{\Delta y}{\Delta x} \), division by zero is undefined). For a vertical line, all points on it have the same x - coordinate.

Step2: Determine the equation

The point given is \( (3,5) \). Since it's a vertical line, the equation is of the form \( x = a \), where \( a \) is the x - coordinate of any point on the line. Here, the x - coordinate of the point \( (3,5) \) is 3, so the equation of the vertical line is \( x = 3 \).

For the hints:

• \( m=\) undefined (because for vertical line, \( \Delta x = 0 \) and \( m=\frac{\Delta y}{\Delta x} \))
• Axis: x - axis (related to vertical line's relation with x - axis, vertical lines are parallel to y - axis and perpendicular to x - axis, but the axis related to the intercept here for vertical line \( x = 3 \), it intersects x - axis at \( (3,0) \))
• Intercept: x - intercept is 3 (the point where the line crosses the x - axis is \( (3,0) \), so x - intercept is 3; there is no y - intercept as the line is parallel to y - axis and never crosses it)
• Equation: \( x = 3 \)

Answer:

The equation of the vertical line passing through \( (3,5) \) is \( x = 3 \).

For the hints:

• \( m=\) undefined
• Axis: x - axis
• Intercept: 3 (x - intercept)
• Equation: \( x = 3 \)