Question

svlc algebra 1a - standard (15260)
introduction to linear functions
which table represents a linear function?

first table (top left):

x	y
2	9
3	5
4	9

second table (top right):

x	y
2	0
3	5
4	10

third table (bottom left):

x	y
2	10
3	20
4	40

fourth table (bottom right):

x	y
2	10
3	-15
4	20

Explanation:

Step1: Recall linear function property

A linear function has a constant rate of change (slope), i.e., $\frac{\Delta y}{\Delta x}$ is constant for consecutive $x$ values.

Step2: Analyze first table

For $x$ from 1 to 2: $\Delta y = 9 - 5 = 4$, $\Delta x = 1$, slope $= 4$.
From 2 to 3: $\Delta y = 5 - 9 = -4$, slope $= -4$. Not constant.

Step3: Analyze second table

From 1 to 2: $\Delta y = 0 - (-5) = 5$, $\Delta x = 1$, slope $= 5$.
From 2 to 3: $\Delta y = 5 - 0 = 5$, slope $= 5$.
From 3 to 4: $\Delta y = 10 - 5 = 5$, slope $= 5$. Constant slope.

Step4: Analyze third table

From 1 to 2: $\Delta y = 10 - 5 = 5$, slope $= 5$.
From 2 to 3: $\Delta y = 20 - 10 = 10$, slope $= 10$. Not constant.

Step5: Analyze fourth table

From 1 to 2: $\Delta y = 10 - (-5) = 15$, slope $= 15$.
From 2 to 3: $\Delta y = -15 - 10 = -25$, slope $= -25$. Not constant.

Answer:

The table with \( x \) values 1, 2, 3, 4 and \( y \) values -5, 0, 5, 10 (second table) represents a linear function.