Which relationship represents a function with a greater rate of change than the function represented above? A B y=(5)/(2)x+3 C y=-(5)/(4)x+4 D

To determine which relationship represents a function with a greater rate of change than the given function, we need to compare the slopes of the linear functions. The slope of a linear function \(y = mx + b\) is represented by \(m\), which indicates the rate of change.<br /><br />Let's analyze the options:<br /><br />- Option B: \(y = \frac{5}{2}x + 3\)<br /> - The slope (rate of change) is \(\frac{5}{2}\).<br /><br />- Option C: \(y = -\frac{5}{4}x + 4\)<br /> - The slope (rate of change) is \(-\frac{5}{4}\).<br /><br />To determine which option has a greater rate of change, we compare the absolute values of the slopes:<br /><br />- \(|\frac{5}{2}| = 2.5\)<br />- \(|-\frac{5}{4}| = 1.25\)<br /><br />Since \(2.5 > 1.25\), the function in Option B (\(y = \frac{5}{2}x + 3\)) has a greater rate of change than the function in Option C (\(y = -\frac{5}{4}x + 4\)).<br /><br />Therefore, the correct answer is **B**.