Question

which statement is true?
the slope of function a is greater than the slope of function b.
the slope of function a is less than the slope of function b.
(graph of function a and table of function b are shown)

Explanation:

Step1: Find slope of Function A

Function A passes through points \((-10, 1)\) and \((10, -1)\) (from the graph). Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
\(m_A = \frac{-1 - 1}{10 - (-10)} = \frac{-2}{20} = -\frac{1}{10}\)

Step2: Find slope of Function B

Function B has points \((-9, -18)\), \((-8, -16)\), \((2, 4)\). Take two points, e.g., \((-9, -18)\) and \((2, 4)\).
\(m_B = \frac{4 - (-18)}{2 - (-9)} = \frac{22}{11} = 2\)? Wait, no, wait. Wait, let's check another pair: \((-8, -16)\) and \((2, 4)\). \(m = \frac{4 - (-16)}{2 - (-8)} = \frac{20}{10} = 2\)? Wait, no, maybe I misread. Wait, the table for Function B: x: -9, -8, 2; y: -18, -16, 4. Wait, let's take \((-9, -18)\) and \((-8, -16)\): \(m = \frac{-16 - (-18)}{-8 - (-9)} = \frac{2}{1} = 2\). Wait, but Function A's slope is \(-\frac{1}{10}\), Function B's slope is 2? No, wait, maybe I made a mistake. Wait, no, the graph of Function A: let's re-examine. Wait, the graph of Function A: when x=-10, y=1; x=10, y=-1? Wait, maybe the points are different. Wait, maybe the graph of Function A passes through (0,0) and (10, -1)? Wait, no, the blue line: let's see, when x=-10, y=1; x=0, y=0; x=10, y=-1. So slope from (-10,1) to (10,-1): \(m = \frac{-1 - 1}{10 - (-10)} = \frac{-2}{20} = -0.1\).

For Function B: let's take (x1,y1)=(-9,-18) and (x2,y2)=(-8,-16). Slope \(m = \frac{-16 - (-18)}{-8 - (-9)} = \frac{2}{1} = 2\). Wait, but that can't be. Wait, maybe the table is x: -9, -8, 2; y: -18, -16, 4. Wait, (2,4) and (-8,-16): \(m = \frac{4 - (-16)}{2 - (-8)} = \frac{20}{10} = 2\). So Function B's slope is 2, Function A's slope is -0.1. Wait, but the options are about which slope is greater. Wait, but maybe I misread the graph. Wait, maybe Function A is a line with negative slope, Function B has positive slope? Wait, no, the options are "The slope of Function A is greater than the slope of Function B" or "The slope of Function A is less than the slope of Function B". Wait, slope of A is -0.1, slope of B is 2? No, that can't be. Wait, maybe I made a mistake in Function A's points. Wait, let's look at the graph again. The blue line (Function A) goes from (-10, 1) to (10, -1)? Wait, no, maybe the points are (-10, 1) and (10, -1)? Wait, no, when x=0, y=0? Wait, the line passes through (0,0). So from (-10,1) to (0,0): slope is (0-1)/(0 - (-10)) = -1/10. From (0,0) to (10,-1): slope is (-1 - 0)/(10 - 0) = -1/10. So slope of A is -1/10.

Function B: let's take two points from the table. Let's take (x=-9, y=-18) and (x=2, y=4). Then slope is (4 - (-18))/(2 - (-9)) = 22/11 = 2. Wait, but that's positive. But maybe the table is misread. Wait, maybe the y-values are negative? Wait, no, the table shows y: -18, -16, 4. Wait, maybe it's a typo, but assuming the table is correct, slope of B is 2, slope of A is -0.1. But -0.1 is greater than 2? No, that's not possible. Wait, no, maybe I messed up the direction. Wait, maybe Function B has a negative slope? Wait, let's check (x=-9, y=-18) and (x=-8, y=-16): the y increases as x increases, so positive slope. Function A has negative slope. So a negative slope is less than a positive slope. Wait, but the options are "The slope of Function A is greater than the slope of Function B" or "The slope of Function A is less than the slope of Function B". Wait, slope of A is -0.1, slope of B is 2. So -0.1 is less than 2? Wait, no, -0.1 is greater than -2, but 2 is positive. Wait, maybe I made a mistake in Function B's slope. Wait, let's recalculate Function B's slope. Let's take (x=-9, y=-18) and (x=2, y=4). \(m = \frac{4 - (-18)}{2 - (-9)} = \frac{22}{11} = 2\). Correct. Function A's slope: from (-10,1) to (10,-1): \(m = \frac{-1 - 1}{10 - (-10)} = \frac{-2}{20} = -0.1\). So -0.1 is less than 2? Wait, no, -0.1 is greater than -2, but 2 is positive. Wait, the question is which statement is true. The options are:

1. The slope of Function A is greater than the slope of Function B.

2. The slope of Function A is less than the slope of Function B.

Wait, slope of A is -0.1, slope of B is 2. So -0.1 < 2, so the second statement is true: "The slope of Function A is less than the slope of Function B."

Wait, but maybe I made a mistake in Function B's slope. Let's check another pair: (x=-8, y=-16) and (x=2, y=4). \(m = \frac{4 - (-16)}{2 - (-8)} = \frac{20}{10} = 2\). Correct. So Function B's slope is 2, Function A's slope is -0.1. So -0.1 is less than 2, so the statement "The slope of Function A is less than the slope of Function B" is true.

Answer:

The slope of Function A is less than the slope of Function B.