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The equation [tex]$y-2=3(x+1)$[/tex] is in point-slope form. Which is the slope-intercept form?

A. [tex]$y=3x+1$[/tex]
B. [tex]$y=3x-3$[/tex]
C. [tex]$y=3x+5$[/tex]

Sagot :

GinnyAnswer
To convert the given equation from point-slope form to slope-intercept form, we need to simplify the equation step by step.

Given equation:
[tex]\[ y - 2 = 3(x + 1) \][/tex]

1. Distribute the 3 on the right side:
[tex]\[ y - 2 = 3 \cdot x + 3 \][/tex]

2. Simplify the equation:
[tex]\[ y - 2 = 3x + 3 \][/tex]

3. Add 2 to both sides to solve for \( y \):
[tex]\[ y = 3x + 3 + 2 \][/tex]

4. Combine like terms:
[tex]\[ y = 3x + 5 \][/tex]

So, the slope-intercept form of the equation is:
[tex]\[ y = 3x + 5 \][/tex]

Therefore, the correct option is:
[tex]\[ y = 3x + 5 \][/tex]
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