What is the slope of the line represented by the equation [tex]$y - 6 = 5(x - 2)$[/tex]?

A. 5
B. 2
C. (No answer provided)
D. 6



Answer :

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].