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Which linear function represents the line given by the point-slope equation [tex]y - 2 = 4(x - 3)[/tex]?

A. [tex]f(x) = 6x - 1[/tex]
B. [tex]f(x) = 8x - 6[/tex]
C. [tex]f(x) = 4x - 14[/tex]
D. [tex]f(x) = 4x - 10[/tex]

Sagot :

GinnyAnswer
To find the linear function that represents the given point-slope equation [tex]\( y - 2 = 4(x - 3) \)[/tex], we need to convert it to the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

Let's proceed step-by-step:

1. Start with the given point-slope equation:
[tex]\[ y - 2 = 4(x - 3) \][/tex]

2. Distribute the 4 on the right side of the equation:
[tex]\[ y - 2 = 4x - 12 \][/tex]

3. Add 2 to both sides to solve for [tex]\( y \)[/tex]:
[tex]\[ y - 2 + 2 = 4x - 12 + 2 \][/tex]
[tex]\[ y = 4x - 10 \][/tex]

So, the linear function in slope-intercept form that represents the given equation is:
[tex]\[ f(x) = 4x - 10 \][/tex]

Therefore, the correct function from the given options is:
[tex]\[ f(x) = 4x - 10 \][/tex]

So, the answer is:
[tex]\[ \boxed{f(x) = 4x - 10} \][/tex]
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