Question

function a and function b are linear functions.
function a
graph of function a on a coordinate plane
function b

x	y
3	14
4	18
5	22

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: Find slope of Function A

From the graph, two points on Function A: let's take \((0, -4)\) and \((2, 2)\) (or other visible points). Slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). So \(m_A=\frac{2 - (-4)}{2 - 0}=\frac{6}{2}=3\).

Step2: Find slope of Function B

Using table for Function B, take points \((3,14)\) and \((4,18)\). Slope \(m_B=\frac{18 - 14}{4 - 3}=\frac{4}{1}=4\)? Wait, no, wait: Wait, another pair: \((4,18)\) and \((5,22)\), \(m_B=\frac{22 - 18}{5 - 4}=4\). Wait, but earlier for Function A, let's recheck. Wait, maybe I picked wrong points. Wait, looking at the graph, when \(x = 0\), \(y=-4\); when \(x = 1\), \(y=-1\)? Wait, no, maybe better points: Let's see the line passes through \((-1, -7)\) and \((1, -1)\)? Wait, no, maybe my first calculation was wrong. Wait, let's take two clear points. Let's see, the line goes from \((-2, -10)\) to \((4, 10)\)? Wait, distance between x: \(4 - (-2)=6\), y: \(10 - (-10)=20\), slope \(20/6\approx3.33\)? Wait, no, maybe I misread. Wait, the graph: when x=0, y=-4; when x=2, y=2 (since from (0,-4) up 6, right 2: 6/2=3). Wait, but Function B: from (3,14) to (4,18): 4/1=4. Wait, but wait, maybe I made a mistake. Wait, no, let's recalculate Function A. Let's take two points: (0, -4) and (1, -1)? Wait, no, the line in the graph: when x=1, y is -1? Wait, no, the grid: each square is 1 unit. So from (0, -4) to (1, -1)? No, that would be slope 3. Wait, but (0, -4) and (2, 2): 2 - (-4)=6, 2 - 0=2, slope 3. Function B: (3,14) to (4,18): 18-14=4, 4-3=1, slope 4. Wait, but then 3 < 4, so slope of A is less than B? Wait, no, wait, maybe I picked wrong points for Function A. Wait, looking at the graph, the line goes from (-2, -10) to (4, 10). So x change: 4 - (-2)=6, y change: 10 - (-10)=20, slope 20/6 ≈ 3.33. Wait, but (3,14) to (5,22): 8/2=4. So 3.33 < 4? Wait, no, maybe my first point for Function A was wrong. Wait, let's check again. The graph: when x= -2, y=-10; x=4, y=10. So slope is (10 - (-10))/(4 - (-2))=20/6≈3.33. Function B: (3,14) to (5,22): (22-14)/(5-3)=8/2=4. So 3.33 < 4, so slope of A is less than B? Wait, but the first calculation with (0,-4) and (2,2) gave 3, which is less than 4. So yes, slope of A (3) is less than slope of B (4). Wait, but wait, maybe I messed up Function A's points. Wait, let's take (1, -1) and (2, 2): slope (2 - (-1))/(2 - 1)=3/1=3. Function B: (3,14) to (4,18): slope 4. So 3 < 4. So the slope of Function A is less than slope of Function B.

Answer:

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