Question

how do i find out if a table is a linear function? i know the formula i just dont know how to figure out if its linear, thanks!

Answer 1

Answer:

Table 3

Explanation:

A linear function has a constant slope.

To determine if the table represents a linear function, find the slope for two different pairs of points.

Table 1

Using the points (1,-2), (2,-6)

$\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-6-(-2)}{2-1}=-6+2=-4$

Using the points (2,-6), (3,-2)

$\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-2-(-6)}{3-2}=-2+6=4$

The slopes are not the same, thus, the function is not linear.

Table 3

Using the points (1,-2), (2,-10)

$\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-10-(-2)}{2-1}=-10+2=-8$

Using the points (2,-10), (3,-18)

$\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-18-(-10)}{3-2}=-18+10=-8$

The slopes are the same, thus, the function is linear.

Table 3 is the correct option.