To determine the slope of the line given by the equation \( y - 5 = -3(x - 17) \), we should recognize that this equation is in the point-slope form of a linear equation.
The point-slope form of a linear equation is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where \( m \) represents the slope of the line, and \((x_1, y_1)\) is any point on the line.
Looking at our specific equation:
[tex]\[ y - 5 = -3(x - 17) \][/tex]
By comparing it to the general point-slope form:
- The expression \( y - 5 \) corresponds to \( y - y_1 \), which signifies that \( y_1 = 5 \).
- The expression \( -3(x - 17) \) corresponds to \( m(x - x_1) \), which shows that \( m = -3 \) and \( x_1 = 17 \).
Thus, the slope \( m \) of the line is clear from this comparison. The value of the slope \( m \) in our equation is:
[tex]\[ -3 \][/tex]
Hence, the slope of the line described by the equation \( y - 5 = -3(x - 17) \) is \(-3\).
The correct answer is:
[tex]\[ \boxed{-3} \][/tex]
