To find the initial value and rate of change of a linear function, we need to calculate the slope of the line, which represents the rate of change, and then use one of the given points to find the initial value.
First, let's calculate the slope. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (2.6, -6) and (3.2, 3), we can plug in these values into the formula:
m = (3 - (-6)) / (3.2 - 2.6)
m = 9 / 0.6
m = 15
So, the slope of the line is 15.
To find the initial value, we can use one of the given points. Let's use the point (2.6, -6).
We can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the initial value.
Plugging in the values we know, we get:
-6 = 15 * 2.6 + b
Simplifying this equation, we get:
-6 = 39 + b
Subtracting 39 from both sides, we find:
b = -45
Therefore, the initial value of the linear function is -45, and the rate of change is 15.
Determine the initial value and the rate of change of the linear function as given in the graph.
(2.6,-6) and (3.2,3)
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