x=-2 output=12 x=1 output =9 x=4 output =6 help me solve
To solve this problem, we need to find the equation that relates the input variable (x) to the output variable.
Let's assume that the equation is a linear equation in the form of y = mx + c, where y represents the output and m and c are constants.
Given the values x = -2 and output = 12, we can substitute these values into the equation to find the value of the constant c:
12 = m(-2) + c
Similarly, for the other two sets of values:
9 = m(1) + c
6 = m(4) + c
We now have a system of three equations with two unknowns (m and c):
-2m + c = 12 (Equation 1)
m + c = 9 (Equation 2)
4m + c = 6 (Equation 3)
To solve this system of equations, we can use elimination or substitution method.
Let's solve using substitution method:
From Equation 2, we can express c in terms of m:
c = 9 - m
Now substitute this expression for c into Equation 1 and Equation 3:
-2m + (9 - m) = 12 (Equation 1)
4m + (9 - m) = 6 (Equation 3)
Simplify the equations:
7 - 3m = 12 (Equation 1)
3m + 9 = 6 (Equation 3)
Solve Equation 1 for m:
-3m = 5
m = -5/3
Substitute this value of m into Equation 3 to find c:
(4 * (-5/3)) + c = 6
-20/3 + c = 6
c = 6 + 20/3
c = 28/3
Therefore, the equation that relates the input variable x to the output variable is:
y = (-5/3)x + 28/3
Now, if you want to find the output for any given value of x, you can substitute that value into this equation and solve for y.