To determine the slope of the line represented by the equation [tex]\( y - 6 = 5(x - 2) \)[/tex], let's start by examining the equation in more detail.
The given equation is in the point-slope form of a line, which is expressed as:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
In the point-slope form:
- [tex]\((x_1, y_1)\)[/tex] is a point on the line.
- [tex]\(m\)[/tex] is the slope of the line.
Let's compare the given equation [tex]\( y - 6 = 5(x - 2) \)[/tex] with the standard form [tex]\( y - y_1 = m(x - x_1) \)[/tex].
From this comparison, we can identify:
- [tex]\( y_1 = 6 \)[/tex]
- [tex]\( x_1 = 2 \)[/tex]
- [tex]\( m = 5 \)[/tex] (the coefficient of [tex]\((x - 2)\)[/tex])
Therefore, the slope of the line is:
[tex]\[ m = 5 \][/tex]
The correct answer is:
D. 5
