[b]Linear functions[/b] are first-degree polynomials defined by the equation y = mx + b. They are characterized[br]by straight lines and a constant rate of change.[br][br][b]Key Features and Parameter Settings[br][/b][br]• [b]The Slope[/b] [i][b](m)[/b][/i]: By setting the value of m, we determine the steepness and direction of the line. In the interactive model, adjusting the Rise and Run sliders directly sets this ratio. For this graph, setting the slope to - 2/3 creates a downward trend where the line drops 2 units for every 3 units it moves right.[br][br]• [b]The Y-intercept[/b] [i][b](b)[/b][/i]: By setting the value of b, we define the vertical starting point where the graph[br]intersects the y-axis. Here, setting & = 1 anchors the line at the coordinate (0, 1).[br][br]•[b] Final Form[/b]: The resulting equation[i], y = -2/3x + 1[/i], is a direct result of these specific parameter settings.[br][br][br]Adjust the slope and y-intercept to see how the line changes. Discover how rise and run affect direction and steepness.

[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]