Question

select all of the statements/graphs that match the equation x = -1.
1 the graph has a slope of zero.
2 graph
3 graph
4 the graph has an undefined slope.
5 the graph is vertical

Explanation:

Step1: Recall the properties of \( x = -1 \)

The equation \( x = -1 \) represents a vertical line. Vertical lines have an undefined slope because the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \) has a denominator of \( 0 \) (since \( x \)-values are constant, \( x_2 - x_1 = 0 \)).

Step2: Analyze each option

• "The graph has a slope of zero": A slope of zero is for horizontal lines (e.g., \( y = k \)), so this is incorrect.
• "The graph has an undefined slope": Correct, as vertical lines have undefined slopes.
• "The graph is vertical": Correct, since \( x = -1 \) is a vertical line.
• For the graphs (assuming graph 3 is the vertical line \( x=-1 \)): The graph with \( x=-1 \) (probably graph 3) and the statements about undefined slope and vertical graph match.

Answer:

The correct options are:

• The graph has an undefined slope.
• The graph is vertical.
• The graph labeled 3 (assuming it's the vertical line \( x = -1 \)).