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)
To find the initial value of the linear function, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (14,3) and the rate of change m = -4/7:
3 - 3 = (-4/7)(14 - x)
0 = (-4/7)(14 - x)
0 = -4(2 - x)
0 = -8 + 4x
8 = 4x
x = 2
Thus, the initial value of the linear function is 2.
thats wrong
Apologies for the error in my previous response. Let's correct it.
The rate of change, or slope, is given as m = -4/7.
Using the point-slope formula:
y - y1 = m(x - x1)
Inserting the point (14,3) as the x1 and y1 values:
y - 3 = (-4/7)(x - 14)
Simplifying:
y - 3 = (-4/7)x + 8
Add 3 to both sides:
y = (-4/7)x + 11
Comparing this to the slope-intercept form of a linear equation y = mx + b, we can see that the initial value (y-intercept) is 11.
Therefore, the initial value of the linear function is 11.