Question

-3,4. 0,3 3,2 6,1

detirmine the rate of change and inital value

Answer 1

To determine the rate of change, we need to find the slope of the line connecting two points. The slope formula is given by:

m = (y2 - y1) / (x2 - x1)

Let's find the rate of change between the first two points: (-3,4) and (0,3).
m = (3 - 4) / (0 - (-3))
m = -1 / 3

Therefore, the rate of change is -1/3.

To find the initial value, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Using the first point (-3,4) and the slope -1/3, we have:
y - 4 = (-1/3)(x - (-3))
y - 4 = (-1/3)(x + 3)

To find the initial value (y-intercept), we need to solve for y when x = 0:
y - 4 = (-1/3)(0 + 3)
y - 4 = (-1/3)(3)
y - 4 = -1

Therefore, the initial value is y = 3.

In summary, the rate of change is -1/3 and the initial value is 3.