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=15.71 b equals 15.71 b=11 b equals 11 b=12.29
To find the initial value (also known as the y-intercept) of the linear function, we need to use the point-slope form of a linear equation: y = mx + b.
Given that the rate of change (or slope) is m = -4/7 and the point (14,3) lies on the line, we can substitute these values into the equation:
3 = (-4/7)(14) + b
To solve for b, we simplify the equation:
3 = -8 + b
3 + 8 = b
11 = b
So, the initial value of the linear function is b = 11. Therefore, the correct response is b = 11.