Interpreting Linear Models in Context

When a linear equation models a real situation (y = mx + b): | Math | Real-world meaning | |---|---| | Slope (m) | The rate of change — how much y changes for each 1-unit increase in x | | Y-intercept (b) | The starting value — the value of y when x = 0 | | X-intercept | The break-even or end point — the value of x when y = 0 | The SAT tests your ability to connect these math concepts to their …

Example: P = 12t - 480 models a company's monthly profit P (dollars) based on t shirts sold. Interpret the slope, y-intercept, and find the x-intercept.

Sometimes the SAT gives you a scenario and asks which equation best models it. Look for: 1. Is there a starting value? → That's b 2. Is there a rate per unit? → That's m 3. Is the quantity increasing or decreasing? → Positive or negative m Common model types: - Cost models: C = text{(cost per unit)} cdot x + text{(fixed cost)} - Distance/motion: d = rt + d_0 - Depreciation: V = V_0 - rt (value …