To find the slope of the line given by the equation [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex], we need to understand the standard form of a linear equation and how slope is represented in such an equation.
### Step-by-Step Solution:
1. Identify the given equation and its format:
The given equation is:
[tex]\[
y - 4 = \frac{5}{2}(x - 2)
\][/tex]
This equation is in the point-slope form of a linear equation, which is generally represented as:
[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. Compare the given equation with the point-slope form:
By comparing [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex] with [tex]\( y - y_1 = m(x - x_1) \)[/tex]:
- [tex]\( y_1 = 4 \)[/tex]
- [tex]\( x_1 = 2 \)[/tex]
- [tex]\( m = \frac{5}{2} \)[/tex]
3. Extract the slope:
From the comparison, we see that the coefficient of [tex]\((x - 2)\)[/tex] is [tex]\(\frac{5}{2}\)[/tex]. This coefficient represents the slope [tex]\(m\)[/tex].
4. State the slope:
Therefore, the slope [tex]\(m\)[/tex] of the line given by the equation [tex]\( y - 4 = \frac{5}{2}(x - 2) \)[/tex] is:
[tex]\[
m = \frac{5}{2}
\][/tex]
5. Convert to decimal form if required:
In decimal form, [tex]\(\frac{5}{2}\)[/tex] is equal to 2.5.
Hence, the slope of the line is [tex]\(\frac{5}{2}\)[/tex] or 2.5.
