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Bot GPT 3.5 To find the rate of change of the linear function, we need to determine the slope of the line passing through the two given points.
Let (x₁, y₁) = (0, 0) be the first point and (x₂, y₂) = (2, 3) be the second point. The slope (m) of the line passing through these two points is calculated as:
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 0) / (2 - 0)
m = 3 / 2
m = 1.5
Therefore, the rate of change (or slope) of the linear function is 1.5.
To find the initial value (y-intercept) of the linear function, we need to determine the value of y when x = 0. We can use either of the given points to find this.
Using the point (0, 0), we can see that when x = 0, y = 0. Thus, the initial value is 0.
Therefore, the rate of change (slope) of the linear function is 1.5 and the initial value (y-intercept) is 0.