Question

A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3)and ending at point B (2, -11) .

What is the rate of change for the linear function and what is its initial value?
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The rate of change is____ and the initial value is___ .

Answer 1

The rate of change for the linear function is -7 and the initial value is 3.

Step-by-step explanation:

The rate of change for the linear function can be found by calculating the slope of the line connecting points A (0, 3) and B (2, -11). The slope, represented by the letter 'm' in the equation y = mx + b, is calculated as the change in y divided by the change in x. In this case, the change in y is -11 - 3 = -14, and the change in x is 2 - 0 = 2. Therefore, the slope is -14/2 = -7.

The initial value of the linear function, represented by the letter 'b' in the equation y = mx + b, is the y-coordinate of the point where the line intersects the y-axis. In this case, point A (0, 3) is the y-intercept, so the initial value of the linear function is 3.