Answered

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Choose a linear function for the line represented by the point-slope equation [tex]y - 5 = 3(x - 2)[/tex].

A. [tex]f(x) = 3x + 1[/tex]
B. [tex]f(x) = 3x - 1[/tex]
C. [tex]f(x) = 8x + 10[/tex]
D. [tex]f(x) = 8x - 10[/tex]

Sagot :

GinnyAnswer
To convert the given point-slope form equation \( y - 5 = 3(x - 2) \) to the slope-intercept form \( y = mx + b \), we need to follow these steps:

1. Distribute the slope \(m\) on the right side:
[tex]\[ y - 5 = 3(x - 2) \][/tex]
Distribute the 3:
[tex]\[ y - 5 = 3x - 6 \][/tex]

2. Isolate \(y\) to get it in the form \( y = mx + b \):
Add 5 to both sides:
[tex]\[ y = 3x - 6 + 5 \][/tex]

3. Simplify the expression:
Combine the constant terms on the right side:
[tex]\[ y = 3x - 1 \][/tex]

So, the linear function in slope-intercept form is:
[tex]\[ f(x) = 3x - 1 \][/tex]

Therefore, the correct choice is:
[tex]\[ f(x) = 3x - 1 \][/tex]
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