Your friend's graph isn't linear; it's exponential. An example of a linear function with initial value 5: y = 2x + 5.
Your friend's error likely stems from misunderstanding the concept of initial value in a linear function. In a linear function, the initial value refers to the y-intercept, which is the point where the graph intersects the y-axis. If the initial value is 5, the function's graph should intersect the y-axis at y = 5.
Your friend's mistake might involve drawing a graph that doesn't intersect the y-axis at y = 5, thus failing to represent a linear function with an initial value of 5.
An example of a graph representing a linear function with an initial value of 5 would be the equation y = mx + 5, where 'm' represents the slope. For instance, let's consider y = 2x + 5. This equation has a slope of 2 and an initial value of 5. When graphed, it intersects the y-axis at y = 5 and maintains a constant slope.
The correct graph should rise by 2 units for every 1 unit it moves to the right (slope of 2) and intersect the y-axis at y = 5. This ensures that the function's initial value, or y-intercept, is indeed 5.