Question

{(-2, 1), (-1, 3), (0, 5), (2, 9)} Is this Exponential,Quatratic,Or Linear or Other?

Answer 1

Answer:

Linear

Step-by-step explanation:

First, calculate the rate of change between each point. Finding this will tell us what type of equation it is.

The formula we will need to use is $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

Let's start with (-2, 1) and (-1, 3).

$\frac{3-1}{-1-(-2)}$

$\frac{2}{1}$

The rate of change between these first two points is 2. Now, let's find the rate of change between (-1, 3) and (0, 5)

$\frac{5-3}{0-(-1)}$

$\frac{2}{1}$

The rate of change between these two points is also 1. When this happens, we know that the line straight.

Linear is just another way to say straight, so this equation is linear.

We know it's not quadratic because if it were, then the rate of change would be gradually increasing or decreasing.

Testing the rate of change of just two points is enough to know that it is linear.