To determine the slope of the line given by the equation [tex]\( y - 3 = -\frac{1}{2}(x - 2) \)[/tex], we should recognize this equation as being in the point-slope form:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
In this form, [tex]\( (x_1, y_1) \)[/tex] is a point on the line, and [tex]\( m \)[/tex] is the slope of the line.
By comparing the given equation [tex]\( y - 3 = -\frac{1}{2}(x - 2) \)[/tex] to the standard point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], we can identify the following:
- The point [tex]\( (x_1, y_1) \)[/tex] is [tex]\((2, 3)\)[/tex].
- The slope [tex]\( m \)[/tex] is given by the coefficient of [tex]\( (x - x_1) \)[/tex], which is [tex]\(-\frac{1}{2}\)[/tex].
Therefore, the slope of the line is:
[tex]\[ -\frac{1}{2} \][/tex]
So, the correct answer is:
[tex]\[ -\frac{1}{2} \][/tex]
This matches the result we would achieve by checking the given options. The slope of the line is [tex]\(-\frac{1}{2}\)[/tex].
