To determine the slope of the line represented by the equation [tex]\( y - 6 = 2(x + 3) \)[/tex], we need to rewrite the equation in the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope.
Let's start by simplifying and rearranging the given equation step-by-step:
1. Start with the original equation:
[tex]\[ y - 6 = 2(x + 3) \][/tex]
2. Distribute the 2 on the right-hand side:
[tex]\[ y - 6 = 2x + 6 \][/tex]
3. To isolate [tex]\( y \)[/tex], add 6 to both sides of the equation:
[tex]\[ y = 2x + 6 + 6 \][/tex]
4. Simplify the right-hand side:
[tex]\[ y = 2x + 12 \][/tex]
Now, the equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex] with [tex]\( m \)[/tex] being the coefficient of [tex]\( x \)[/tex]. From the equation [tex]\( y = 2x + 12 \)[/tex], we see that the coefficient of [tex]\( x \)[/tex] is 2.
Hence, the slope [tex]\( m \)[/tex] of the line is:
[tex]\[ \boxed{2} \][/tex]
