Question

graph a line that is perpendicular to the given line. determine the slope of the given line and the one you graphed in simplest form. click and drag on the graph to draw a line.

click and drag to plot a perpendicular line. the line will change colors when a parallel or perpendicular line is drawn accurately.

Explanation:

Identify the given line and its slope

The given line is a horizontal line passing through \(y = -5\).
A horizontal line has a change in \(y\) of \(0\) for any change in \(x\).
Therefore, the slope of the given line is:

$$m_1 = 0$$

Determine the slope of the perpendicular line

Two lines are perpendicular if their slopes are negative reciprocals, or if one is horizontal and the other is vertical.
Since the given line is horizontal, any line perpendicular to it must be a vertical line.
A vertical line has a constant \(x\)-value, meaning the change in \(x\) is \(0\).
Since division by zero is undefined, the slope of a vertical line is undefined.
Therefore, the slope of the perpendicular line is:

$$m_2 = \text{Undefined}$$

Graph the perpendicular line

To graph a line perpendicular to the horizontal line \(y = -5\), we can draw any vertical line.
For example, we can draw the vertical line passing through the origin, which is the \(y\)-axis (\(x = 0\)), or any other vertical line such as \(x = 2\).
Let's choose the vertical line \(x = 2\) to clearly show a distinct perpendicular line on the grid.
This line passes through points such as \((2, 0)\) and \((2, 5)\).

Answer:

• Slope of the given line: \(0\)
• Slope of the perpendicular line: Undefined
• Graph description: Draw any vertical line on the coordinate plane (for example, the line \(x = 2\) passing vertically through \(2\) on the \(x\)-axis).