answer !!!
so basically:
To determine the relationship between the x- and y-values and write an equation, let's analyze the given data points!!
From the table:
When x = 3, y = -12
When x = 1, y = -4
When x = 2, y = -8
When x = 4, y = -16
To find the relationship between x and y, we can calculate the difference between the x-values and the corresponding y-values:
When x increases by 1 (from 1 to 2), y decreases by 4 (from -4 to -8).
Similarly, when x increases by 1 (from 2 to 3), y decreases by 4 (from -8 to -12).
And when x increases by 1 (from 3 to 4), y decreases by 4 (from -12 to -16).
From these observations, we can conclude that for every increase of 1 in x, there is a decrease of 4 in y. This indicates a linear relationship between x and y.
To find the equation representing this relationship, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (m) is -4, as for every increase of 1 in x, y decreases by 4.
To find the y-intercept (b), we can pick any point from the given data. Let's use the point (1, -4). Plugging these values into the equation, we have:
-4 = -4(1) + b
-4 = -4 + b
b = 0
Therefore, the equation that represents the relationship between x and y is y = -4x.
Note: The other options given (y = 4x, y = -3x + 1, and y = x) do not accurately represent the relationship between x and y based on the given data.
(p.s i used..partial ai for this eheh-)