To determine the initial value and rate of change, we need to algebraically represent the relationship between the x-values and y-values of the given points.
Let's first find the equation of the line passing through the points (0,0) and (0.5,1):
We can use the slope-intercept form of a linear equation, y = mx + b, where m represents the rate of change (slope) and b represents the initial value (y-intercept).
First, calculate the slope (rate of change) using the formula:
m = (y2 - y1) / (x2 - x1)
Given points: (0,0) and (0.5,1)
m = (1 - 0) / (0.5 - 0)
m = 1 / 0.5
m = 2
Now we know that the rate of change (slope) is 2.
Using one of the given points, substitute the values into the slope-intercept form and solve for b:
0 = 2(0) + b
0 = 0 + b
b = 0
The initial value (y-intercept) is 0.
Therefore, the equation of the line passing through the points (0,0) and (0.5,1) is y = 2x + 0, which simplifies to y = 2x.
Since the point (-1.5, -3) is not on this line, we can conclude that it is not part of the given linear relationship. Hence, we cannot determine the initial value and rate of change using all three given points.
The points on the graph are (-1.5,-3), (0,0) and (0.5,1) Determan the initial value and rate change
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