Question

select all of the statements/graphs that match the equation y = 5. the graph has a slope of zero. the graph is horizontal. graph graph the graph is vertical.

Explanation:

Step1: Analyze the equation \( y = 5 \)

The equation \( y = 5 \) represents a horizontal line because for any value of \( x \), \( y \) remains 5. The slope of a horizontal line is calculated using the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For two points \((x_1, 5)\) and \((x_2, 5)\) on the line, \( m=\frac{5 - 5}{x_2 - x_1}=\frac{0}{x_2 - x_1} = 0 \), so the slope is 0.

Step2: Evaluate each statement/graph

• "The graph has a slope of zero": Since \( y = 5 \) is horizontal with slope 0, this is correct.
• "The graph is horizontal": A line with equation \( y = k \) (constant) is horizontal, so this is correct.
• The third option (the graph with a horizontal red line, likely at \( y = 5 \)): Matches \( y = 5 \), so correct.
• The fourth option (vertical line): A vertical line has equation \( x = k \), not \( y = 5 \), so incorrect.
• "The graph is vertical": Incorrect, as \( y = 5 \) is horizontal.

Answer:

• "The graph has a slope of zero" (checked)
• "The graph is horizontal" (checked)
• The third graph (the one with the horizontal red line, likely at \( y = 5 \)) (checked)