Find the initial value of the linear function, given that the rate of change is m=−4
over 7 , and (14,3) is an (x,y) value of the linear function.(1 point)
Responses
b=11
b equals 11
b=−5
b equals negative 5
b=15.71
b equals 15.71
b=12.29
b equals 12.29
To find the initial value of the linear function, we can use the point-slope form of a linear equation, which is given by:
y - y1 = m(x - x1)
Where m is the rate of change and (x1, y1) is a point on the line.
In this case, m = -4/7 and the point (14, 3) is on the line.
So, plugging in the values into the point-slope form:
3 - y1 = (-4/7)(14 - x1)
Simplifying:
3 - y1 = (-4/7)(14) + (4/7)x1
3 - y1 = -8/7 + (4/7)x1
3 - y1 = (4/7)x1 - 8/7
To find the initial value (y-intercept), we need to find the value of y1 when x1 = 0.
So, setting x1 = 0:
3 - y1 = (4/7)(0) - 8/7
3 - y1 = 0 - 8/7
3 - y1 = -8/7
To isolate y1, subtract 3 from both sides:
-y1 = -8/7 - 21/7
-y1 = -29/7
Divide both sides by -1 to solve for y1:
y1 = 29/7
Therefore, the initial value (y-intercept) of the linear function is b = 29/7.