Find the initial value of the linear function, given that the rate of change is m=−47 , and (14,3) is an (x,y) value of the linear function.(1 point)Responsesb=15.71b equals 15.71b=12.29  b equals 12.29b=−5b equals negative 5b=11

1 answer

To find the initial value (intercept) of the linear function, we can use the slope-intercept form of a linear equation, which is:

\[ y = mx + b \]

Where:

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

Given:

  • The slope \( m = -47 \)
  • The point \( (14, 3) \)

We can plug these values into the equation to solve for \( b \):

  1. Substitute \( x = 14 \), \( y = 3 \), and \( m = -47 \):

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

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

\[ -47(14) = -658 \]

So now the equation becomes:

\[ 3 = -658 + b \]

  1. Add 658 to both sides to solve for \( b \):

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

Thus, the initial value (y-intercept) of the linear function is \( b = 661 \).

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