Solutions for Lesson 7 Homework on Linear and Nonlinear Functions

1. Start by carefully analyzing each problem. Identify whether the equation represents a straight or curved graph, and consider how the slope or curvature impacts the solution. This approach is crucial for distinguishing between different types of equations.

2. For straight line equations, focus on the slope and intercept. Use the slope-intercept form (y = mx + b) to identify key values such as the slope (m) and y-intercept (b). Make sure to apply these values to plot the graph accurately.

3. For curved graphs, consider the degree of the equation. Higher degree equations tend to create more complex curves. Analyze the general shape of the graph and the turning points. For example, quadratic equations form parabolas, while cubic equations create curves with more inflections.

4. Check each solution by plotting the values. A great way to verify your answers is by graphing them. Compare your graph with the given function to ensure it matches the expected behavior, whether it’s a straight line or curve.

5. Review any patterns that emerge in similar problems. Many problems in this category will follow similar patterns in their solutions, so identifying these can help you work through the material more quickly. If you notice a consistent relationship between coefficients and the graph, apply that knowledge to solve future problems.