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 \( b \):
- Substitute \( x = 14 \), \( y = 3 \), and \( m = -47 \):
\[ 3 = -47(14) + b \]
- Calculate \( -47(14) \):
\[ -47(14) = -658 \]
So now the equation becomes:
\[ 3 = -658 + b \]
- 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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