To determine the equation of a line, we use the slope-intercept form of the equation, which is given by:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept, which is the point where the line crosses the y-axis.
In this problem, we are provided with:
- A slope [tex]\( m = 6 \)[/tex].
- A y-intercept [tex]\( b = -2 \)[/tex].
Following the formula [tex]\( y = mx + b \)[/tex], we substitute the given values:
1. Substitute [tex]\( m \)[/tex] with 6:
[tex]\[ y = 6x + b \][/tex]
2. Then, substitute [tex]\( b \)[/tex] with -2:
[tex]\[ y = 6x - 2 \][/tex]
Thus, the equation of the line is:
[tex]\[ y = 6x - 2 \][/tex]
Therefore, the correct answer is:
B. [tex]\( y = 6x - 2 \)[/tex]
