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=15.71
b=11
To find the initial value (b) of the linear function, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the rate of change and (x1, y1) is a point on the line.
Using the given information, m = -4/7 and (14,3) is a point on the line, we can substitute these values into the point-slope form:
3 - y1 = (-4/7)(14 - x1)
Simplifying the equation, we get:
3 - y1 = (-4/7)(14) + (4/7)x1
3 - y1 = -8 + (4/7)x1 [Simplifying (-4/7)(14) to -8]
Now, let's solve for y1:
y1 = 3 + 8 - (4/7)x1
y1 = 11 - (4/7)x1
We can see that the initial value (b) is 11.
Therefore, the correct answer is: b = 11.