To find the slope of the line represented by the equation [tex]\( y - 4 = \frac{5}{2} (x - 2) \)[/tex]:
1. Identify the form of the equation:
The equation is given in the point-slope form of a line, which is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where:
- [tex]\( (x_1, y_1) \)[/tex] is a point on the line,
- [tex]\( m \)[/tex] is the slope of the line.
2. Compare with the given equation:
Compare [tex]\( y - y_1 = m(x - x_1) \)[/tex] with the given equation [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex]:
- [tex]\( y_1 = 4 \)[/tex]
- [tex]\( x_1 = 2 \)[/tex]
- [tex]\( m = \frac{5}{2} \)[/tex]
3. Identify the slope:
From the comparison, the slope [tex]\( m \)[/tex] of the line is:
[tex]\[
\frac{5}{2}
\][/tex]
Therefore, the slope of the line whose equation is [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex] is [tex]\( \boxed{2.5} \)[/tex].
