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)
The rate of change, also known as the slope, represents the change in the y-values for every unit change in x. In this case, the rate of change is m = -47.
To find the initial value of the linear function, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where (x1, y1) represents the given point (14, 3).
Substituting the values, we have:
y - 3 = -47(x - 14)
Now, we can simplify the equation:
y - 3 = -47x + 658
Adding 3 to both sides:
y = -47x + 661
Therefore, the initial value of the linear function is 661.