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.(1 point) Responses b=−5 b equals negative 5 b=12.29 b equals 12.29 b=15.71 b equals 15.71 b=11 b equals 11

Answer 1

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 m is the rate of change and (x1, y1) are the coordinates of the given point.

In this case, m = -4/7 and the point is (14, 3).

Plugging in these values, we get:

y - 3 = (-4/7)(x - 14)

Next, we can simplify the equation by distributing -4/7 to (x - 14):

y - 3 = (-4/7)x + 8

Adding 3 to both sides of the equation, we get:

y = (-4/7)x + 11

The initial value of the linear function is the y-intercept, which is the constant term in the equation. In this case, the constant term is 11.

Therefore, the initial value of the linear function is b = 11.