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
To find the initial value of the linear function, we need to use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Using the given values, we have:
y - 3 = (-4/7)(x - 14)
Next, we can distribute the -4/7 to simplify the equation:
y - 3 = (-4/7)(x) + (4/7)(14)
Further simplifying, we have:
y - 3 = (-4/7)x + 8
Finally, let's isolate y by adding 3 to both sides of the equation:
y = (-4/7)x + 11
The initial value of the linear function is 11.