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

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}}=(-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}}=(-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}}=(-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}}=(-18-(-10))/(3-2)=-18+10=-8`

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

Table 3 is the correct option.