Respuesta :
The linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].
What is a linear function?
- The word linear function in mathematics refers to two distinct but related concepts.
- A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
To find the linear function which represents the line given by the point-slope equation:
Given: [tex]y-8=\frac{1}{2} (x-4)[/tex]
Distribute the right side:
[tex]y-8=\frac{1}{2} (x)-\frac{1}{2} 4\\y-8=\frac{1}{2} x-2[/tex]
Adds 8 on both sides:
[tex]y=\frac{1}{2}x-2+8\\y=\frac{1}{2}x+6[/tex]
Convert to function notation:
[tex]f(x)=y\\f(x)=\frac{1}{2} x+6[/tex]
Therefore, the linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].
Know more about linear functions here:
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The complete question is given below:
Which linear function represents the line given by the point-slope equation y – 8 = y minus 8 equals start fraction one-half end fraction left-parenthesis x minus 4 right-parenthesis. (x – 4)?
A) F(x) = f(x) equals StartFraction one-half EndFraction x plus 4.X + 4
B) f(x) = f(x) equals StartFraction one-half EndFraction x plus 6.
C) X + 6 f(x) = f(x) equals StartFraction one-half EndFraction x minus 10.X –10
D) f(x) = f(x) equals StartFraction one-half EndFraction x minus 12.X – 12
