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What is the correct slope-intercept form of the equation [tex]$y + 16 = 3(x - 0)$[/tex]?

A. [tex]$y = 3x + 16$[/tex]
B. [tex][tex]$y = 3x - 16$[/tex][/tex]
C. [tex]$y = \frac{3}{16}x$[/tex]
D. [tex]$y = 16 - 3x$[/tex]


Sagot :

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.