Linear Landscapes: Exploring Slopes and Intercepts Cont.

With the table complete, it’s clear how the pathway’s elevation changes with each step. But the city council has further concerns about the long-term impact of the pathway on the park’s landscape, particularly regarding erosion. The city council asks Jada to explain the significance of the pathway’s slope.

With the council’s concerns about erosion addressed, Jada shifts focus to the structural integrity of the pathway. She knows that the points where the path crosses the axes are critical for maintenance and support. Jada needs to find where the pathway would cross the [latex]x[/latex]-axis, as this is where additional support may be needed.

Now that you’ve determined where the pathway intersects the [latex]x[/latex]-axis, Jada presents you with a new challenge. She has a second pathway to consider and needs to understand how its characteristics compare to the first. Jada presents a graph with two pathways and asks you to compare their slopes and [latex]y[/latex]-intercepts.

With your help, Jada has successfully planned the park’s pathways and presented her findings to the city council. Your ability to interpret linear functions and their graphs has been instrumental in ensuring the park’s design is both beautiful and functional. Great work!