1. The problem asks which graph represents a linear function increasing at a constant rate. 2. A linear function has the form $$y = mx + b$$ where $$m$$ is the slope (rate of change) and $$b$$ is the y-intercept. 3. An increasing linear function has a positive slope $$m > 0$$, meaning the line rises from left to right at a constant rate. 4. Analyze each graph: - Graph A passes through (-5,-5) and (6,5). Calculate slope: $$m = \frac{5 - (-5)}{6 - (-5)} = \frac{10}{11} > 0$$, so it is increasing linearly. - Graph B is a curve, not a line, so it is nonlinear. - Graph C passes through (6,-6) and (-6,6). Calculate slope: $$m = \frac{6 - (-6)}{-6 - 6} = \frac{12}{-12} = -1 < 0$$, so it is decreasing. - Graph D passes through (-6,-6) and (6,6). Calculate slope: $$m = \frac{6 - (-6)}{6 - (-6)} = \frac{12}{12} = 1 > 0$$, so it is increasing linearly. 5. Both Graph A and Graph D show increasing linear functions, but Graph D is exactly $$y = x$$, a classic example of a linear function increasing at a constant rate. Final answer: Graph D represents a linear function increasing at a constant rate.