the image shows a line going from around (-5.2, 3.5) to (5.2,-1.5) there are three plotted points which are: (-3,2.5) and (0,1) and (2,0)
the initial value is (blank). And the rate of change is (blank)
In order to determine the initial value and the rate of change, we can use the slope-intercept form of a linear equation, which is y = mx + b.
To find the rate of change (m), we need to calculate the slope of the line. The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given coordinates (x1, y1) = (-5.2, 3.5) and (x2, y2) = (5.2, -1.5):
m = (-1.5 - 3.5) / (5.2 - (-5.2))
m = (-5) / (10.4)
m = -0.5
So, the rate of change is -0.5.
To find the initial value (b), we can substitute the coordinates of one of the points into the equation and solve for b. Let's use the point (0, 1):
1 = (-0.5)(0) + b
1 = b
Therefore, the initial value is 1.
Final Answer:
- The initial value is 1.
- The rate of change is -0.5.