Short Answer 
The initial value of function G is -1, as it passes through the point (0, -1). Similarly, the initial value of function H is also -1, calculated using the slope from two points, leading to the conclusion that both functions have the same initial value.
Step 1: Understand the Initial Value of Function G
The initial value of a function is determined by its y-intercept, which occurs when x equals zero. For function G, it is specified that it passes through the point (0, -1). Thus, the initial value of function G is clearly identified as -1.
Step 2: Calculate the Initial Value of Function H
To find the initial value of function H, we must first calculate the slope using two given points: (8, 3) and (10, 4). The slope (m) can be determined using the formula: m = (y2 – y1) / (x2 – x1). After plugging in the coordinates, we find:
- Slope (m) = (4 – 3) / (10 – 8) = 1 / 2
Next, we can use the slope-intercept form to find the equation of the line and subsequently the y-intercept, which turns out to be -1 as well.
Step 3: Compare the Initial Values
Now that we have the initial values for both functions, we can summarize our findings: the initial value of function G is -1 and the initial value of function H is also -1. Therefore, since both initial values are equal, we conclude that Kelly’s assertion is incorrect, as both functions share the same initial value.