Slope and y-intercepts Quick Check 3 of 53 of 5 Items Question 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 b=11 b equals 11 b=15.71 b equals 15.71 b=12.29 b equals 12.29 b=−5 b equals negative 5
To find the initial value of the linear function, we need to use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Given that the rate of change is m = -47 and (14,3) is an (x,y) value of the linear function, we can substitute these values into the point-slope form:
3 - y1 = -47(14 - x1)
Simplifying the equation, we get:
3 - y1 = -658 + 47x1
Rearranging the equation to isolate y1, we get:
y1 = 47x1 - 655
Therefore, the initial value of the linear function is -655.
So, the correct answer is b=−5 as it represents the initial value of the linear function.