Question

Determine whether the table of values below represents a linear function. If it represents a linear function, write the function. If it does not represent a linear function, explain why not.

Answer 1

Answer:

The equation of a linear function is:

• $y = 2x+4$

Step-by-step explanation:

Given the table

x                    y

-10               -16

-3                 -2

1                    6

2                   8

Determining the slope between the points (-10, -16), (-3, -2)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-10,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-2\right)$

$m=\frac{-2-\left(-16\right)}{-3-\left(-10\right)}$

$m=2$

Determining the slope between the points (-3, -2), (1, 6)

$m=\frac{6-\left(-2\right)}{1-\left(-3\right)}$

$m=2$

Determining the slope between the points (1, 6),(2, 8)

$m=\frac{8-6}{2-1}$

$m = 2$

As the slope between the points is the same. Thus, the table represents the linear function.

Using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

substituting the values m = 2 and any point let say (1, 6)

$y - 6 = 2(x-1)$

$y-6 = 2x-2$

$y = 2x-2+6$

$y = 2x+4$

Therefore, the equation of a linear function is:

• $y = 2x+4$