(-3,2.5) (0,1) (2,0) what is the initial value and the rate if change

1 answer

To determine the initial value and rate of change, we need to find the equation of the line that passes through the given points.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope and b represents the y-intercept (initial value).

First, let's find the slope (rate of change) using two points:

m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-3,2.5) and (x2, y2) = (0,1)

m = (1 - 2.5) / (0 - (-3))
m = (-1.5) / (3)
m = -0.5

Now that we have the slope, we can find the initial value (y-intercept) by substituting one of the given points into the slope-intercept form and solving for b:

1 = (-0.5)(0) + b
1 = 0 + b
b = 1

Therefore, the equation of the line passing through the given points is y = -0.5x + 1.

The initial value is 1 and the rate of change is -0.5.