Find the initial value of the linear function, given that the rate of change is m=−4/7, and (14,3) is an (x,y) value of the linear function.
The rate of change of a linear function is also known as the slope. So we have a slope of m = -4/7.
We can use the slope-intercept form of a linear function, which is y = mx + b, where m is the slope and b is the y-intercept (the initial value).
We are given the point (14,3) is on the linear function, so we can substitute these values into the equation:
3 = (-4/7)(14) + b
To solve for b, we can simplify the equation:
3 = -8 + b
Now, we can add 8 to each side to isolate b:
11 = b
Therefore, the initial value (y-intercept) of the linear function is b = 11.