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Rewrite the equation [tex]y - 8 = 2(x + 4)[/tex] into slope-intercept form [tex](y = mx + b)[/tex].

A. [tex]y = 2x[/tex]
B. [tex]y = 2x + 8[/tex]
C. [tex]y = 2x + 12[/tex]
D. [tex]y = 2x + 16[/tex]

Sagot :

GinnyAnsweridn
To rewrite the equation [tex]\( y - 8 = 2(x + 4) \)[/tex] into slope-intercept form [tex]\( y = mx + b \)[/tex], follow these steps:

1. Start with the given equation:
[tex]\[ y - 8 = 2(x + 4) \][/tex]

2. Expand the right-hand side:
[tex]\[ y - 8 = 2 \cdot x + 2 \cdot 4 \][/tex]
[tex]\[ y - 8 = 2x + 8 \][/tex]

3. Isolate [tex]\( y \)[/tex] on the left side to put the equation in the form [tex]\( y = mx + b \)[/tex]:
[tex]\[ y = 2x + 8 + 8 \][/tex]
[tex]\[ y = 2x + 16 \][/tex]

The simplified form of the equation is:
[tex]\[ y = 2x + 16 \][/tex]

This equation is now in the slope-intercept form [tex]\( y = mx + b \)[/tex] where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

Hence, the best answer is:
[tex]\[ \boxed{D. \; y = 2x + 16} \][/tex]
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