To determine the slope of the line given by the equation [tex]\( y - 3 = -\frac{1}{2}(x - 2) \)[/tex], we should first recognize the structure of the equation. This is in the point-slope form, which is written as:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
In this formula, [tex]\( m \)[/tex] represents the slope of the line, while [tex]\( (x_1, y_1) \)[/tex] represents a specific point on the line. Comparing the given equation [tex]\( y - 3 = -\frac{1}{2}(x - 2) \)[/tex] to the point-slope form, we can identify the slope [tex]\( m \)[/tex].
The coefficient of [tex]\( (x - 2) \)[/tex] is the slope [tex]\( m \)[/tex]. Here, the coefficient is [tex]\( -\frac{1}{2} \)[/tex].
Thus, the slope of the line is:
[tex]\[ m = -\frac{1}{2} \][/tex]
Therefore, the slope of the line is [tex]\( -0.5 \)[/tex].
So, the result is not [tex]\(-2\)[/tex] nor [tex]\(\frac{1}{2}\)[/tex], but rather the correct slope is [tex]\(-0.5\)[/tex]. Note that the given choices do not include the correct slope.
