To determine the slope of the line given by the equation [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex], let’s follow these steps:
1. Identify the Form of the Equation: The given equation is in the point-slope form, which is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.
2. Extract the Slope: By comparing the given equation [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex] with the point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], we can see that [tex]\( m \)[/tex], the slope, is the coefficient of [tex]\((x - x_1) \)[/tex].
3. Identify the Coefficient of [tex]\((x-2)\)[/tex]: In our equation, the term multiplying [tex]\((x - 2)\)[/tex] is [tex]\(\frac{5}{2}\)[/tex].
Therefore, the slope of the line is:
[tex]\[
\boxed{2.5}
\][/tex]
