Question

which graph represents the equation $y = -3x$ ?

Explanation:

Step1: Analyze the equation form

The equation \( y = -3x \) is in slope - intercept form \( y=mx + b \), where \( m=-3 \) (slope) and \( b = 0 \) (y - intercept). So the line should pass through the origin \((0,0)\) and have a negative slope (since \( m=-3<0 \)), meaning it goes down from left to right.

Step2: Check each graph

• First graph: The line has a positive slope (goes up from left to right), so it's not correct.
• Second graph: The line does not pass through the origin, so it's not correct.
• Third graph: The line has a positive slope, so it's not correct.
• Fourth graph: The line passes through the origin \((0,0)\) and has a negative slope (goes down from left to right), which matches the equation \( y=-3x \).

Answer:

The Right Graph (the fourth graph from the left)