Question

for each function, state whether it is linear.
function 1
{(5, -3), (6, -7), (7, -11), (8, -15)}
○linear
○not linear
function 2
{(2, -5), (3, -2), (4, -1), (5, 1)}
○linear
○not linear
function 3

x	y
-5	2
-3	-2
-1	-1
1	0

○linear
○not linear
function 4

x	y
-4	3
0	5
4	7
8	9

○linear
○not linear

Explanation:

Function 1

Step1: Calculate the slope between consecutive points.

For points \((5, -3)\) and \((6, -7)\), the slope \(m_1=\frac{-7 - (-3)}{6 - 5}=\frac{-4}{1}=-4\).
For points \((6, -7)\) and \((7, -11)\), the slope \(m_2=\frac{-11 - (-7)}{7 - 6}=\frac{-4}{1}=-4\).
For points \((7, -11)\) and \((8, -15)\), the slope \(m_3=\frac{-15 - (-11)}{8 - 7}=\frac{-4}{1}=-4\).

Step2: Check if slopes are equal.

Since \(m_1 = m_2 = m_3=-4\), the function has a constant slope.

Step1: Calculate the slope between consecutive points.

For points \((2, -5)\) and \((3, -2)\), the slope \(m_1=\frac{-2 - (-5)}{3 - 2}=\frac{3}{1}=3\).
For points \((3, -2)\) and \((4, -1)\), the slope \(m_2=\frac{-1 - (-2)}{4 - 3}=\frac{1}{1}=1\).

Step2: Check if slopes are equal.

Since \(m_1 = 3\) and \(m_2 = 1\) are not equal, the function does not have a constant slope.

Step1: Calculate the slope between consecutive points.

For points \((-5, 2)\) and \((-3, -2)\), the slope \(m_1=\frac{-2 - 2}{-3 - (-5)}=\frac{-4}{2}=-2\).
For points \((-3, -2)\) and \((-1, -1)\), the slope \(m_2=\frac{-1 - (-2)}{-1 - (-3)}=\frac{1}{2}=0.5\).

Step2: Check if slopes are equal.

Since \(m_1=-2\) and \(m_2 = 0.5\) are not equal, the function does not have a constant slope.

Answer:

Linear

Function 2