The function representing the given values has a constant rate of change. It can be written as a linear equation in the form y = mx + b, where m is the constant rate of change and b is the y-intercept.
Using the given values, we can find the constant rate of change (m) by calculating the difference in y-values and dividing it by the difference in x-values. Let's compare two sets of points:
(x1, y1) = (-3, 12)
(x2, y2) = (1, -4)
Change in y = y2 - y1 = -4 - 12 = -16
Change in x = x2 - x1 = 1 - (-3) = 4
Constant rate of change (m) = Change in y / Change in x = -16 / 4 = -4
So the linear equation representing the given values is y = -4x + b. To find the y-intercept (b), we can substitute the values of one point into the equation. Let's use the point (x1, y1) = (-3, 12):
12 = -4(-3) + b
12 = 12 + b
b = 0
Therefore, the function representing the given values with a constant rate of change is y = -4x + 0, which simplifies to y = -4x.
x
-3,-1,0,1,3,4
y
12,4,0,-4,-12,-16
_ is a function with a constant rate of change
1 answer
1 answer