To determine the slope of the line represented by the equation [tex]\( y - 6 = 5(x - 2) \)[/tex], let's proceed step by step.
1. Identify the form of the equation given:
The equation provided is [tex]\( y - 6 = 5(x - 2) \)[/tex].
This is a form of the point-slope equation of a line, which is generally written as:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [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]\( y - 6 = 5(x - 2) \)[/tex] with [tex]\( y - y_1 = m(x - x_1) \)[/tex], we can see that:
[tex]\[
y_1 = 6 \quad \text{and} \quad x_1 = 2
\][/tex]
Also, it is clear that:
[tex]\[
m = 5
\][/tex]
3. Conclusion:
Therefore, the slope [tex]\( m \)[/tex] of the line represented by the given equation is [tex]\( 5 \)[/tex].
4. Choose the correct answer:
Given the options:
- A. 5
- B. 2
- C. (not given)
- D. 6
The correct answer is [tex]\(\boxed{5}\)[/tex].
