Question

for each function, state whether it is linear.
function 1
{(-4, 5), (-2, 10), (0, 17), (2, 25)}
○linear
○not linear
function 2
{(0, 0), (4, 5), (8, 10), (12, 15)}
○linear
○not linear
function 3

x	y
-2	4
-1	9
0	16
1	25

○linear
○not linear
function 4

x	y
5	-2
8	-3
11	0
14	3

○linear
○not linear

Explanation:

Function 1

Step1: Calculate the slope between the first two points

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(-4, 5)$ and $(-2, 10)$:
$m_1 = \frac{10 - 5}{-2 - (-4)} = \frac{5}{2} = 2.5$

Step2: Calculate the slope between the second and third points

For points $(-2, 10)$ and $(0, 17)$:
$m_2 = \frac{17 - 10}{0 - (-2)} = \frac{7}{2} = 3.5$

Step3: Compare the slopes

Since $m_1
eq m_2$ (2.5 ≠ 3.5), the function is not linear.

Function 2

Step1: Calculate the slope between the first two points

For points $(0, 0)$ and $(4, 5)$:
$m_1 = \frac{5 - 0}{4 - 0} = \frac{5}{4} = 1.25$

Step2: Calculate the slope between the second and third points

For points $(4, 5)$ and $(8, 10)$:
$m_2 = \frac{10 - 5}{8 - 4} = \frac{5}{4} = 1.25$

Step3: Calculate the slope between the third and fourth points

For points $(8, 10)$ and $(12, 15)$:
$m_3 = \frac{15 - 10}{12 - 8} = \frac{5}{4} = 1.25$

Step4: Compare the slopes

Since $m_1 = m_2 = m_3$ (all 1.25), the function is linear.

Function 3

Step1: Calculate the slope between the first two points

For points $(-2, 4)$ and $(-1, 9)$:
$m_1 = \frac{9 - 4}{-1 - (-2)} = \frac{5}{1} = 5$

Step2: Calculate the slope between the second and third points

For points $(-1, 9)$ and $(0, 16)$:
$m_2 = \frac{16 - 9}{0 - (-1)} = \frac{7}{1} = 7$

Step3: Compare the slopes

Since $m_1
eq m_2$ (5 ≠ 7), the function is not linear.

Function 4

Answer:

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