To determine the initial value and the rate of change of the linear function, we need to find the equation of the line that passes through the given points.
The slope or rate of change (m) of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (2,3) and (0,0), we have:
m = (0 - 3) / (0 - 2)
m = -3 / -2
m = 3/2
The initial value or y-intercept (b) can be found by substituting one of the points into the slope-intercept form of a linear equation, y = mx + b, and solving for b.
Using the point (2,3):
3 = (3/2)(2) + b
3 = 3 + b
b = 3 - 3
b = 0
The equation of the line is y = (3/2)x.
Therefore, the initial value is 0, and the rate of change is 3/2.
Determine the initial value and the rate of change of the linear function as given in the graph.
2,3 0,0
The initial value is , and the rate of change is .
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