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: a line on a coordinate plane with x and y axes, and a table for function b with x values -1, 2, 5 and y values -5, 7, 19)

Explanation:

Step1: Find slope of Function A

Function A is a line passing through \((0,0)\) and \((2,1)\) (from graph). Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\). So \(m_A=\frac{1 - 0}{2 - 0}=\frac{1}{2}=0.5\).

Step2: Find slope of Function B

Function B has points \((-1, -5)\), \((2,7)\), \((5,19)\). Using two points, e.g., \((-1, -5)\) and \((2,7)\). Slope \(m_B=\frac{7 - (-5)}{2 - (-1)}=\frac{12}{3}=4\).

Step3: Compare slopes

\(m_A = 0.5\), \(m_B = 4\). So \(m_A < m_B\), meaning the slope of Function A is less than that of Function B.

Answer:

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