Write the equation for the following relation. Include all of your work in your final answer. Submit your solution.
P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12),
y increases by 4 when x increases by 1. So, look for something like
y = 4x+b
Now, when x=1, y=0, so we end up with
y = 4x-4
line of form y = m x + b
m = (Y2/Y1)(X2-X1)
= (4-0)/(2-1)
= 4 check with other points (like (12-0)/(4-1) )
y = 4 x + b
put a point in to find b
0 = 4(1) + b
b = -4
so
y = 4 x - 4
To find the equation for the given relation, we need to determine the pattern or relationship between the x and y values.
Given the points in the relation P:
(1, 0), (2, 4), (3, 8), (4, 12)
We can observe that for each x value, the corresponding y value is increasing by 4. Hence, there is a constant rate of change of 4 between y values.
We can also notice that the y value is 4 times the x value. Therefore, the equation for the given relation is:
y = 4x
So, the equation for the relation P is y = 4x.
To find the equation for the given relation, we can observe the pattern in the coordinates provided.
We can see that as the value of x increases by 1, the value of y increases by 4. This indicates a linear relationship between x and y.
To find the equation, we need to determine the slope and y-intercept.
Let's calculate the slope (m):
m = (change in y) / (change in x)
= (4 - 0) / (2 - 1)
= 4 / 1
= 4
Since the slope is constant throughout, the equation will be of the form: y = mx + b, where m is the slope and b is the y-intercept.
Now let's find the y-intercept:
Using one of the given points of (1, 0), we can substitute the values into the equation and solve for b:
0 = 4(1) + b
0 = 4 + b
b = -4
Therefore, the equation for the given relation is:
y = 4x - 4
So, the final answer is y = 4x - 4.