Graph Selection 657020

1. The problem is to identify the graph of the linear equation $$y = -2.5x - 3$$. 2. The equation is in slope-intercept form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept. 3. Here, the slope $$m = -2.5$$ and the y-intercept $$b = -3$$. 4. The y-intercept means the line crosses the y-axis at the point $$(0, -3)$$. 5. The slope $$-2.5$$ means for every increase of 1 in $$x$$, $$y$$ decreases by 2.5. 6. Check each graph's y-intercept and slope: - Graph 1: y-intercept at $$-3$$, slope negative, points approximately $(-1, -0.5)$ and $(1, -5)$. Calculate slope between these points: $$\frac{-5 - (-0.5)}{1 - (-1)} = \frac{-4.5}{2} = -2.25$$, close to $$-2.5$$. - Graph 2: y-intercept at $$3$$, slope positive, so not matching. - Graph 3: y-intercept at $$3$$, slope negative, no match. - Graph 4: y-intercept at $$-3$$, slope positive, no match. 7. Graph 1 matches the y-intercept and has a slope close to $$-2.5$$. Final answer: The correct graph is Graph 1 (top-left).