• Express a linear function using an equation, words, tables, and graphs
• Determine whether a linear function is increasing, decreasing, or constant.
• Calculate and interpret slope
• Find the x-intercept of a linear function given its equation

Linear Landscapes: Exploring Slopes and Intercepts

Jada, an urban planner, is designing a new park in the city. The park’s pathways are represented by linear functions on her map. She needs to calculate various aspects of these pathways to ensure they meet the city’s design standards.

 

Jada shows you the blueprint of a pathway represented by the equation [latex]y=2x-5[/latex] . She asks you to graph this function and determine its key features.

The slope and [latex]y[/latex]-intercept of the graph can tell more than just the direction and starting point of the path. They also give insight into how accessible the path will be for visitors. Jada needs to ensure the pathway is accessible, which means it cannot be too steep.

Understanding the slope’s impact on accessibility, Jada now wants to communicate these changes to the city council in a clear and concise manner. A table would be the perfect way to visualize the elevation changes over the distance of the pathway.