Question

function a and function b are linear functions.
function a (graph of a line) and function b (table with x and y values: x=-6,y=-24; x=3,y=12; x=5,y=20)
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 two points from the graph, e.g., \((0, 3)\) and \((-6, 0)\). Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\). So \(m_A=\frac{3 - 0}{0 - (-6)}=\frac{3}{6}=\frac{1}{2}\)? Wait, no, let's check again. Wait, the graph: when \(x = -6\), \(y = 0\); when \(x = 0\), \(y = 3\)? Wait, no, looking at the graph, the line passes through \((-6, 0)\) and \((0, 3)\)? Wait, no, maybe better points. Wait, the y-intercept is at \((0, 3)\), and it crosses the x-axis at \((-6, 0)\). So slope \(m_A=\frac{3 - 0}{0 - (-6)}=\frac{3}{6}=\frac{1}{2}\)? Wait, no, wait, let's take another pair. When \(x = 6\), \(y = 6\)? Wait, maybe I made a mistake. Wait, the graph: from \((-6, 0)\) to \((0, 3)\), the rise is 3, run is 6, so slope is \(3/6 = 1/2\)? Wait, no, wait, the line: when x increases by 6 (from -6 to 0), y increases by 3 (from 0 to 3). So slope is 3/6 = 0.5.

Step2: Calculate slope of Function B

Use two points from the table, e.g., \((-6, -24)\) and \((3, 12)\). Slope \(m_B=\frac{12 - (-24)}{3 - (-6)}=\frac{36}{9}=4\). Wait, or \((3, 12)\) and \((5, 20)\): \(m_B=\frac{20 - 12}{5 - 3}=\frac{8}{2}=4\). So \(m_A = 0.5\), \(m_B = 4\). So \(m_A < m_B\).

Answer:

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