Question

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.

Answer 1

The rate of change of a linear function is given by the slope, which in this case is m = -4/7.

We can write the equation of the linear function in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept (the initial value we are trying to find).

Using the given point (14,3), we can substitute these values into the equation to solve for b:

3 = (-4/7)(14) + b

Multiply -4/7 by 14:

3 = -8 + b

Now, we can isolate b by adding 8 to both sides:

11 = b

Therefore, the initial value (y-intercept) of the linear function is 11.