Find the initial value of the linear function, given that the rate of change is m=−47 , and (14,3) is an (x,y) value of the linear function.(1 point) Responses b=11 b equals 11 b=12.29 b equals 12.29 b=−5 b equals negative 5 b=15.71

1 answer

To find the initial value of the linear function, we can use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the rate of change.

In this case, we have m = -47 and the point (14,3). Plugging these values into the equation, we get y - 3 = -47(x - 14).

Expanding and simplifying the equation, we have y - 3 = -47x + 658.

To find the initial value, we need to find the value of y when x = 0. Substituting x = 0 into the equation, we get y - 3 = -47(0) + 658, which simplifies to y - 3 = 658.

Solving for y, we have y = 661.

Therefore, the initial value of the linear function is b = 661.