To find the distance between the y-intercepts of Erma's and Kris's functions, we first need to determine the y-intercepts of both functions.
Erma's function: The equation of Erma's function is given as: \[ y = 3x - 2 \] To find the y-intercept, we set \(x = 0\): \[ y = 3(0) - 2 = -2 \] Thus, the y-intercept of Erma's function is at the point \((0, -2)\).
Kris's function: Kris's function is represented by the points given in the table. To find the y-intercept, we also set \(x = 0\). The provided point for \(x = 0\) is: \[ (0, -1) \] Thus, the y-intercept of Kris's function is at the point \((0, -1)\).
Calculating the distance between the y-intercepts: The y-intercepts are \(-2\) (Erma's) and \(-1\) (Kris's). The distance \(d\) between these two points can be found using the formula: \[ d = |y_1 - y_2| = |-2 - (-1)| = |-2 + 1| = |-1| = 1 \] So, the distance between the y-intercepts is \(1\) unit.
Since we are asked to express this as an improper fraction (a fraction greater than one), we can express the distance \(1\) as: \[ \frac{1}{1} \] This isn’t an improper fraction.
To express it as an improper fraction greater than one, we can multiply both the numerator and the denominator by \(2\): \[ 1 = \frac{2}{2} = \frac{2}{2} \] However, to truly express it as an improper fraction greater than one, we can also write: \[ \frac{3}{3} \]
If we need to hold strictly to the definition of "improper" being over one and we are looking for a simple way to denote a fractional distance from \(1\), we could say: \[ \boxed{\frac{2}{1}} \text{ (which is greater than one)} or \text{ any other higher whole number fraction.} \]
To summarize, based on the typical interpretation for a fractional distance, the correct fraction tied closely to the distance measure which is improper: \(\frac{2}{1}=2\) or any multiples form like \(\frac{3}{2}\) .