Question

function a and function b are linear functions. function a (graph of a line on a coordinate plane) function b (table with x and y values: x=-9,y=-5; x=-6,y=-4; x=9,y=1) 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, Function A passes through points \((0, -5)\) and \((6, 10)\) (we can also use other points, but these are clear). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). So, \(m_A=\frac{10 - (-5)}{6 - 0}=\frac{15}{6}=\frac{5}{2}=2.5\).

Step2: Find slope of Function B

Using two points from Function B's table, say \((-9, -5)\) and \((-6, -4)\). The slope \(m_B=\frac{-4 - (-5)}{-6 - (-9)}=\frac{1}{3}\approx0.333\).

Step3: Compare slopes

Since \(2.5>\frac{1}{3}\), the slope of Function A is greater than that of Function B.

Answer:

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