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Which equation describes the same line as [tex]\( y - 5 = -2(x + 4) \)[/tex]?

A. [tex]\( y = -2x - 8 \)[/tex]

B. [tex]\( y = -2x - 3 \)[/tex]

C. [tex]\( y = -2x + 9 \)[/tex]

D. [tex]\( y = -2x - 2 \)[/tex]

Sagot :

GinnyAnsweridn
To convert the given equation [tex]\( y - 5 = -2(x + 4) \)[/tex] into the slope-intercept form [tex]\( y = mx + b \)[/tex], follow these steps:

1. Start with the original equation:
[tex]\[ y - 5 = -2(x + 4) \][/tex]

2. Distribute the [tex]\(-2\)[/tex] on the right-hand side:
[tex]\[ y - 5 = -2x - 8 \][/tex]

3. To isolate [tex]\( y \)[/tex], add [tex]\( 5 \)[/tex] to both sides of the equation:
[tex]\[ y = -2x - 8 + 5 \][/tex]

4. Simplify the constant terms on the right-hand side:
[tex]\[ y = -2x - 3 \][/tex]

So, the equation in slope-intercept form is:
[tex]\[ y = -2x - 3 \][/tex]

Comparing this with the given options:

A. [tex]\( y = -2x - 8 \)[/tex] (not the same)
B. [tex]\( y = -2x - 3 \)[/tex] (same as what we derived)
C. [tex]\( y = -2x + 9 \)[/tex] (not the same)
D. [tex]\( y = -2x - 2 \)[/tex] (not the same)

Therefore, the correct answer is:

B. [tex]\( y = -2x - 3 \)[/tex]
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