Final answer:
To demonstrate changes in a line's y-intercept while maintaining a slope of 1, you can use a graph where the line shifts vertically up or down the y-axis without altering the slope. This can be visualized using simulation tools like Graphing Lines that allow interactive adjustments to the line's characteristics.
Step-by-step explanation:
To create an interactive that shows how a line with slope 1 changes as its y-intercept changes, you can use the concept of slope-intercept form, which is represented as y = mx + b, where m is the slope and b is the y-intercept. When the slope (m) is constant at 1, the line will have a 45-degree angle relative to the axes. Changing the y-intercept (b) will shift the line up or down the y-axis, without altering the slope. This can be visualized through a graph.
For better understanding, consider this example: if the initial y-intercept is 3, the line will cross the y-axis at (0,3). If you increase the y-intercept to 5, the line will shift upwards, and now intersect the y-axis at (0,5). This shift is vertical because the slope remained constant.
In virtual physics or math simulation tools, students can often adjust these values dynamically to see how the graph changes. One such tool is Graphing Lines, which provides an interactive experience to visualize these changes in real-time.