Find the rate of change and the initial value of the linear function given as these values: (-3,2.5) (0,1) (2,0)
To find the rate of change and the initial value of the linear function, we need to determine the equation of the line that passes through the points (-3,2.5), (0,1), and (2,0).
First, let's find the slope (rate of change) of the line using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (-3,2.5) and (0,1):
slope = (1 - 2.5) / (0 - (-3))
slope = (-1.5) / (3)
slope = -0.5
Now, we have the slope of the line.
Next, we can determine the initial value (y-intercept) of the line. To do this, we can substitute the coordinates of any of the given points into the equation y = mx + b and solve for b.
Using the point (0,1):
1 = -0.5(0) + b
1 = 0 + b
b = 1
Therefore, the equation of the line can be written as y = -0.5x + 1.
So, the rate of change is -0.5 and the initial value is 1.