To find the initial value and rate of change, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the rate of change (also known as the slope) and b is the initial value (also known as the y-intercept).
First, let's find the rate of change (m). The formula for finding the slope between two points is:
m = (y2 - y1) / (x2 - x1)
Using the given points (2.6, -6) and (3.2, 3):
m = (3 - (-6)) / (3.2 - 2.6)
m = 9 / 0.6
m = 15
So, the rate of change is 15.
Next, let's use one of the given points, (2.6, -6), to find the initial value (b). We'll substitute the coordinates (x = 2.6, y = -6) into the slope-intercept form of the equation:
-6 = 15(2.6) + b
-6 = 39 + b
b = -6 - 39
b = -45
Therefore, the initial value is -45.
In summary:
The rate of change is 15.
The initial value is -45.
The points on the graph are (2.6,-6) and (3.2,3) Determan the initial value and rate change
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