Brismithperiotidn
Answered

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Choose the linear function that corresponds to 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 :

GinnyAnsweridn
To choose the linear function that represents the line given by the point-slope equation [tex]\( y - 5 = 3(x - 2) \)[/tex], we can convert this equation into the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

Here are the steps:

1. Start with the given point-slope equation:

[tex]\[ y - 5 = 3(x - 2) \][/tex]

2. Distribute the slope value (3) on the right side of the equation:

[tex]\[ y - 5 = 3x - 6 \][/tex]

3. Isolate [tex]\( y \)[/tex] by adding 5 to both sides of the equation:

[tex]\[ y = 3x - 6 + 5 \][/tex]

4. Simplify the expression on the right side:

[tex]\[ y = 3x - 1 \][/tex]

Therefore, the linear function in slope-intercept form that matches the given point-slope equation is:

[tex]\[ f(x) = 3x - 1 \][/tex]

Among the provided options, the correct choice is:

[tex]\[ f(x) = 3x - 1 \][/tex]
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