To determine the initial value and rate of change of a linear function, we can use the formula for the slope-intercept form of a linear function:
y = mx + b,
where m is the rate of change (the slope) and b is the initial value (the y-intercept).
First, let's find the rate of change (m). Rate of change is determined by the difference in y-coordinates divided by the difference in x-coordinates between two points on the graph.
m = (change in y) / (change in x)
m = (-4/3 - (-10/3)) / (-1 - (-4))
m = (-4/3 + 10/3) / (-1 + 4)
m = (6/3) / (3)
m = 2/1
m = 2
Now, let's find the initial value (b) by substituting the coordinates of one of the points into the equation:
-4 = 2(-1) + b
-4 = -2 + b
b = -4 + 2
b = -2
Therefore, the initial value of the linear function is -2, and the rate of change is 2.
Determine the initial value and the rate of change of the linear function as given in the graph.
(-4,-10/3) (-1,-4/3)
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