Find the initial value of the linear function, given that the rate of change is m=−47

Question

, 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 equals 12.29

b=15.71
b equals 15.71

b=11
b equals 11

Answer 1

To find the initial value \( b \) of the linear function represented in the slope-intercept form \( y = mx + b \) where \( m \) is the slope (given as \( -47 \)) and the point (14, 3) is on the line, we can substitute the values into the equation.

1. Substituting the point into the equation: We know that at \( x = 14 \), \( y = 3 \).

   \[ 3 = -47(14) + b \]

2. Calculate \( -47(14) \):

   \[ -47 \times 14 = -658 \]

3. Substitute back:

   \[ 3 = -658 + b \]

4. Solve for \( b \):

   \[ b = 3 + 658 \] \[ b = 661 \]

It seems that none of the provided options match the calculated value. Please check the values given in the question and confirm if there are any additional constraints or correct choices that lead to a value near 661. If solely working from the options given, based on the calculation of the function, it appears there might be an issue with the options provided.