Write the equation for the following relation, Submit your solution.
P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}
(n+1,4n) from n = 0 to n --->oo
seems to work
in other words
y = 4(n-1) = 4x - 4
To find the equation for the given relation P, we need to determine the pattern or rule that relates the x-values to the corresponding y-values.
We can observe that the y-values increase by 4 each time the x-value increases by 1. This suggests that there is a linear relationship between the x-values and y-values.
To find the equation, let's represent the x-value as 'x' and the corresponding y-value as 'y'. We'll need to find the slope (m) and the y-intercept (b) to write the equation in the form y = mx + b.
First, let's find the slope (m):
We can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Taking two sets of points, (1, 0) and (2, 4), we can calculate the slope as follows:
m = (4 - 0) / (2 - 1)
= 4 / 1
= 4
The slope (m) is 4.
Next, let's find the y-intercept (b):
We can use the point-slope form of a line equation, which is y - y1 = m(x - x1) and substitute the values of one of the given points (let's use (1,0)) to find the y-intercept.
Using the point (1, 0) and the slope (m = 4), we can substitute these values into the point-slope form equation:
y - 0 = 4(x - 1)
y = 4x - 4
Therefore, the equation for the given relation P is:
y = 4x - 4.
Hence, the solution to the problem is y = 4x - 4.