find the graph for this direct variation equation. y = -2x

Explanation:

Step1: Identify slope - intercept form

The equation $y = - 2x$ is in the form $y=mx + b$, where $m=-2$ (slope) and $b = 0$ (y - intercept).

Step2: Analyze slope and y - intercept

Since $b = 0$, the line passes through the origin $(0,0)$. The slope $m=-2$ means for every 1 unit increase in $x$, $y$ decreases by 2 units.

Step3: Check graphs

The first graph has a steeper negative - slope and passes through the origin. The second graph has a steeper negative - slope but does not pass through the origin. The third graph has a less steep negative - slope. The correct graph is the first one as it has a slope of - 2 and passes through the origin.

Answer:

The first graph.