Question

function 1: {(-5, -3), (-4, -5), (-3, -7), (-2, -9)}; linear (selected), not linear (unselected)
function 2: {(5, -2), (8, -1), (11, 0), (14, 1)}; linear (unselected), not linear (selected)
function 3:

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

linear (unselected), not linear (selected)
function 4:

x	y
3	1
7	1
11	1
15	1

linear (selected), not linear (unselected)

Explanation:

Step1: Check Function 1 linearity

Calculate the rate of change (slope) between consecutive points:
Slope between $(-5,-3)$ and $(-4,-5)$: $\frac{-5 - (-3)}{-4 - (-5)} = \frac{-2}{1} = -2$
Slope between $(-4,-5)$ and $(-3,-7)$: $\frac{-7 - (-5)}{-3 - (-4)} = \frac{-2}{1} = -2$
Slope between $(-3,-7)$ and $(-2,-9)$: $\frac{-9 - (-7)}{-2 - (-3)} = \frac{-2}{1} = -2$
All slopes are equal, so it is linear.

Step2: Check Function 2 linearity

Calculate the rate of change between consecutive points:
Slope between $(5,-2)$ and $(8,-1)$: $\frac{-1 - (-2)}{8 - 5} = \frac{1}{3}$
Slope between $(8,-1)$ and $(11,0)$: $\frac{0 - (-1)}{11 - 8} = \frac{1}{3}$
Slope between $(11,0)$ and $(14,1)$: $\frac{1 - 0}{14 - 11} = \frac{1}{3}$
All slopes are equal, so it is linear (the current selection is incorrect).

Step3: Check Function 3 linearity

Calculate the rate of change between consecutive points:
Slope between $(-3,5)$ and $(-2,3)$: $\frac{3 - 5}{-2 - (-3)} = \frac{-2}{1} = -2$
Slope between $(-2,3)$ and $(-1,0)$: $\frac{0 - 3}{-1 - (-2)} = \frac{-3}{1} = -3$
Slopes are not equal, so it is not linear.

Step4: Check Function 4 linearity

Calculate the rate of change between consecutive points:
Slope between $(3,1)$ and $(7,1)$: $\frac{1 - 1}{7 - 3} = \frac{0}{4} = 0$
Slope between $(7,1)$ and $(11,1)$: $\frac{1 - 1}{11 - 7} = \frac{0}{4} = 0$
Slope between $(11,1)$ and $(15,1)$: $\frac{1 - 1}{15 - 11} = \frac{0}{4} = 0$
All slopes are equal, so it is linear.

Answer:

• Function 1: Linear
• Function 2: Linear
• Function 3: Not linear
• Function 4: Linear