Which of the relationships below represents a function with a greater slope than the function y=3 x-3 ? A B C x & y 4 & 27 8 & 51 12 & 75 16 & 90 D x & y 0 & -4 4 & 3 8 & 10 12 & 17

To determine which relationship represents a function with a greater slope than the function \( y = 3x - 3 \), we need to calculate the slope of each given relationship and compare it to the slope of the given function, which is 3.<br /><br />**Option C:**<br /><br />The table provides points \((4, 27)\), \((8, 51)\), \((12, 75)\), and \((16, 90)\).<br /><br />Calculate the slope using any two points. Let's use \((4, 27)\) and \((8, 51)\):<br /><br />\[<br />\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{51 - 27}{8 - 4} = \frac{24}{4} = 6<br />\]<br /><br />**Option D:**<br /><br />The table provides points \((0, -4)\), \((4, 3)\), \((8, 10)\), and \((12, 17)\).<br /><br />Calculate the slope using any two points. Let's use \((0, -4)\) and \((4, 3)\):<br /><br />\[<br />\text{slope} = \frac{3 - (-4)}{4 - 0} = \frac{7}{4} = 1.75<br />\]<br /><br />Comparing the slopes:<br />- The slope of the function \( y = 3x - 3 \) is 3.<br />- The slope for Option C is 6.<br />- The slope for Option D is 1.75.<br /><br />Therefore, Option C represents a function with a greater slope than the function \( y = 3x - 3 \).