Question

function a and function b are linear functions.
function a
x | y
2 | -1
4 | 3
8 | 11
function b
graph of function b
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.

Explanation:

Step1: Calculate slope of Function A

Use slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Take points (2, -1) and (4, 3):
$m_A = \frac{3 - (-1)}{4 - 2} = \frac{4}{2} = 2$.

Step2: Calculate slope of Function B

From the graph, two points: (0, 5) and (1, 10) (approx, or use (0,5) and (-1,0)):
Take (0, 5) and (-2, -5): $m_B = \frac{-5 - 5}{-2 - 0} = \frac{-10}{-2} = 5$? Wait, no, better points: (0,5) and (1,10)? Wait, graph: when x=0, y=5? Wait, no, looking at the graph, the line passes through (0,5)? Wait, no, the y-intercept: the line goes through (0,5)? Wait, no, let's check the grid. The line passes through (0,5) and (1,10)? Wait, no, when x=1, y=10? Wait, the top point is (1,10)? Wait, the graph: the blue line goes from (-5, -10) to (1,10)? Wait, no, let's use two clear points. Let's take (0,5) and (1,10): slope is (10-5)/(1-0)=5. Wait, but earlier Function A slope is 2. Wait, no, maybe I made a mistake. Wait, Function A: points (2,-1), (4,3), (8,11). Let's recalculate slope of A: (3 - (-1))/(4-2)=4/2=2; (11-3)/(8-4)=8/4=2. So slope of A is 2. Now Function B: let's take two points from the graph. The line passes through (0,5) and (1,10)? Wait, no, when x=0, y=5? Wait, the grid: each square is 1 unit. The line goes through (0,5) and (1,10)? Wait, no, the top point is (1,10)? Wait, the graph shows the line going from (-5, -10) to (1,10). Wait, slope is (10 - (-10))/(1 - (-5))=20/6≈3.33? No, that's not right. Wait, maybe better to use (0,5) and (-1,0): slope is (0-5)/(-1-0)=5. Wait, but maybe I misread the graph. Wait, the y-intercept: the line crosses the y-axis at (0,5)? Wait, the grid: the y-axis has 0, 2, 4, 6, 8, 10. So the line passes through (0,5) and (1,10)? Wait, no, when x=1, y=10? Then slope is 5. But Function A's slope is 2. So slope of B is 5, which is greater than A's 2. Wait, but the options: "The slope of Function A is less than the slope of Function B." So that's the true statement. Wait, but let's recalculate Function B's slope correctly. Let's take two points from the graph: (0,5) and (1,10) – no, wait, the line goes through (0,5) and (1,10)? Wait, the graph: when x=0, y=5; x=1, y=10? Then slope is 5. Function A's slope is 2. So 2 < 5, so slope of A is less than slope of B.

Answer:

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