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

1 answer

The initial value of the linear function can be found using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

In this case, you are given m = -47 and (14,3) is a point on the line.

Using the point-slope form with (14,3) as the point and -47 as the slope, we have:

y - 3 = -47(x - 14)

Expanding and simplifying the equation, we get:

y - 3 = -47x + 658

y = -47x + 661

The initial value of the linear function is the y-intercept, which is the value of y when x = 0. Therefore, substitute x = 0 into the equation:

y = -47(0) + 661

y = 661

So, the initial value of the linear function is 661.