Determine a relationship between the x- and y- values in the equation {(0,1), (1,0), (2, -1), (3, -2)}. Write an equation......y=?

gobbler

To determine the relationship between the x- and y-values in the given equation, we can observe the pattern and look for any consistent changes.

Looking at the x-values, we can see that they increase by 1 each time: 0, 1, 2, 3.

Looking at the corresponding y-values, we can see that they decrease by 1 each time: 1, 0, -1, -2.

Based on this pattern, we can conclude that the relationship between the x- and y-values is a linear relationship, with a negative slope of -1.

To write the equation, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

where (x₁, y₁) is a point on the line and m is the slope.

Taking the first point (0, 1) as (x₁, y₁), and substituting the slope -1:

y - 1 = -1(x - 0)

Simplifying, we have:

y - 1 = -x

To isolate y, we can move -1 to the right side:

y = -x + 1

Therefore, the equation that represents the relationship between the x- and y-values is y = -x + 1.

y=2+3