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)
b=11
b=12.29
b=15.71
b=−5
y = -(4/7) x + b
3 = -(4/7) 14 + b
3 = -8 + b
b = 11
Determine the initial value and the rate of change of the linear function as given in the graph. (1 point) Responses The initial value is −23, and the rate of change is 23. The initial value is negative Start Fraction 2 over 3 End Fraction , and the rate of change is Start Fraction 2 over 3 End Fraction . The initial value is −2, and the rate of change is 23. The initial value is negative 2 , and the rate of change is Start Fraction 2 over 3 End Fraction . The initial value is 23, and the rate of change is −23. The initial value is Start Fraction 2 over 3 End Fraction , and the rate of change is negative Start Fraction 2 over 3 End Fraction . The initial value is 16, and the rate of change is 32.
To find the initial value of the linear function, we need to use the slope-intercept form of a linear equation:
y = mx + b
where "m" is the rate of change (slope) and "b" is the initial value (y-intercept).
In this case, we are given that the rate of change (m) is -4/7. We are also given a point on the line, (14, 3).
To find the initial value (b), we can substitute the x and y values from the given point into the equation:
3 = (-4/7)(14) + b
Simplifying this equation:
3 = -8 + b
To isolate "b", we add 8 to both sides of the equation:
3 + 8 = b
11 = b
Therefore, b = 11, which means the initial value of the linear function is 11.
So, the correct answer is b = 11.