Sure, let's transform the given equation [tex]\( y + 16 = 3(x - 0) \)[/tex] into the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
1. Start with the given equation:
[tex]\[
y + 16 = 3(x - 0)
\][/tex]
2. Simplify inside the parentheses:
Since [tex]\( (x - 0) \)[/tex] simplifies to [tex]\( x \)[/tex], the equation becomes:
[tex]\[
y + 16 = 3x
\][/tex]
3. Isolate [tex]\( y \)[/tex] on the left-hand side by subtracting 16 from both sides:
[tex]\[
y + 16 - 16 = 3x - 16
\][/tex]
Simplifying this, we get:
[tex]\[
y = 3x - 16
\][/tex]
So, the slope-intercept form of the equation is [tex]\( y = 3x - 16 \)[/tex].
Therefore, the correct answer is:
[tex]\[
y = 3x - 16
\][/tex]
This corresponds to the second option in the given list.
