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=15.71
b equals 15.71

b=12.29
b equals 12.29

b=11
b equals 11

b=−5

Answer 1

To find the initial value \( b \) of the linear function, we can use the point-slope form of the linear equation:

\[ y = mx + b \]

where:

• \( m \) is the slope (rate of change),
• \( (x, y) \) is a point on the line,
• \( b \) is the y-intercept (initial value).

From the problem, we know:

• \( m = -47 \)
• The point \( (14, 3) \) means \( x = 14 \) and \( y = 3 \).

Substituting these values into the equation:

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

Calculating \( -47(14) \):

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

So, the equation becomes:

\[ 3 = -658 + b \]

Now, solve for \( b \):

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

Now checking the options given, this value does not match any of the responses provided. Please verify the values or the premise.