x=-2 output=12 x=1 output =9 x=4 output =6 help me solve
To solve this problem, we need to analyze the relationship between the input (x) and output values. Based on the given information, we can see that as x increases, the output decreases.
Let's find the pattern between the input and output values.
When x = -2, the output is 12.
When x = 1, the output is 9.
When x = 4, the output is 6.
To determine the equation that relates x and the output, we can start by noticing that the output decreases by 3 each time the value of x increases by 1.
So, we can infer that for each unit increase in x, the output decreases by 3 units. Hence, the equation can be expressed as:
output = k * (x - h),
where k is the constant rate of change (which we determined to be -3), and h is the x-value when the output is zero.
To find the value of h, we need to find the x-value when the output is zero. Setting the output to zero and solving for x:
0 = k * (x - h)
0 = -3 * (x - h)
We can plug in the values of x and the output for any given pair (let's use x = 4 and output = 6) to solve for h:
0 = -3 * (4 - h)
0 = -12 + 3h
12 = 3h
h = 4
Now that we have the value of h, we can substitute it back into the equation:
output = -3 * (x - 4)
To verify the equation, let's test it with the other given pairs:
x = -2:
output = -3 * (-2 - 4) = -3 * (-6) = 18
x = 1:
output = -3 * (1 - 4) = -3 * (-3) = 9
x = 4:
output = -3 * (4 - 4) = -3 * (0) = 0
As we can see, the equation output = -3 * (x - 4) satisfies all the given pairs.