To determine the slope of the line given the equation [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex], let's analyze the equation step by step.
1. Identify the form of the equation:
The given equation [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex] is in the point-slope form, which is written as:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Here, [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
2. Compare the given equation to the point-slope form:
Let's rewrite the provided equation:
[tex]\[
y - 4 = \frac{5}{2}(x - 2)
\][/tex]
By comparing this to the general point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], we can deduce the following:
- [tex]\( y_1 = 4 \)[/tex]
- [tex]\( x_1 = 2 \)[/tex]
- [tex]\( m = \frac{5}{2} \)[/tex]
3. The value of [tex]\( m \)[/tex] is the slope of the line. Therefore, from the equation [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex], we see that the slope [tex]\( m \)[/tex] is:
[tex]\[
m = \frac{5}{2}
\][/tex]
4. Simplify the slope if necessary:
Often, slopes are presented in decimal form as well. So, converting [tex]\( \frac{5}{2} \)[/tex] to a decimal gives:
[tex]\[
\frac{5}{2} = 2.5
\][/tex]
Thus, the slope of the line whose equation is [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex] is [tex]\( 2.5 \)[/tex].
