write a function rule the relates the inout X and output Y:
(0,1), (1,4), (2,7), (3,10)
please help! I can't get this one..
BTW, I meant, "write a function rule that relates the input X and output Y" =)
as the x's increase by 1, the y's increase by 3
so the slope = 3/1 = 3
the equation must be
y = 3x + b, where b is the y-intercept
but we can see from (0,1) that the y-intercept is 1
so...
y = 3x + 1
thank you very much =)
To find a function rule that relates the input X and output Y, we can look for a pattern in the given data points. Let's analyze the given data points: (0,1), (1,4), (2,7), (3,10).
We can observe that the output Y increases by 3 each time the input X increases by 1. So, for each increase of 1 in X, there is an increase of 3 in Y.
To express this pattern as a function rule, we can state that Y is equal to 3 times X plus a constant value. We will need to find the constant value to complete the function rule.
Let's calculate the constant value using one of the given data points, such as (0,1). When X is 0, Y should be equal to 1.
Plugging in the values into the function rule: Y = 3X + C,
1 = 3(0) + C,
1 = 0 + C,
C = 1.
Now we have the constant value C, which is 1. The completed function rule that relates X and Y is:
Y = 3X + 1.
To verify this rule, you can substitute the other given data points into the equation and see if it holds true.