Question

function a and function b are linear functions.
function a
$y = 3x + 4$
function b

x	y
-1	-4
3	16
4	21

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

Function A is \( y = 3x + 4 \), in slope - intercept form \( y=mx + b \) (where \( m \) is slope), so slope of A, \( m_A=3 \).

Step2: Find slope of Function B

For a linear function, slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Take two points from Function B's table, e.g., \( (x_1,y_1)=(- 1,-4) \) and \( (x_2,y_2)=(3,16) \).
\( m_B=\frac{16-(-4)}{3 - (-1)}=\frac{16 + 4}{3+1}=\frac{20}{4}=5 \).

Step3: Compare slopes

Since \( 3<5 \), i.e., \( m_A

Answer:

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