Question

which graph shows the equation $y = -2x - 4$

Explanation:

Step1: Analyze the slope and y-intercept

The equation is \( y = -2x - 4 \), which is in slope - intercept form \( y=mx + b \), where \( m=-2 \) (slope) and \( b = - 4 \) (y - intercept). A negative slope means the line should be decreasing (going from top - left to bottom - right). The y - intercept is at \( (0,-4) \), so the line crosses the y - axis at \( y=-4 \).

Step2: Evaluate each graph

• Graph A: Check the slope and y - intercept. The line has a negative slope (decreasing) and crosses the y - axis at \( y=-4 \), which matches the equation \( y=-2x - 4 \).
• Graph B: The line has a positive slope (increasing), which does not match the negative slope of \( y=-2x - 4 \), so we can eliminate B.
• Graph C: The line has a positive slope (increasing), which does not match the negative slope of \( y=-2x - 4 \), so we can eliminate C.
• Graph D: The y - intercept of this line is at a positive value (not \( y = - 4 \)), so it does not match the equation \( y=-2x - 4 \), so we can eliminate D.

Answer:

A. The graph labeled A