Question

Which linear function represents the line given by the point-slope equation y – 8 = y minus 8 equals startfraction one-half endfraction left-parenthesis x minus 4 right-parenthesis.(x – 4)?

Answer 1

The linear function which represents the line given by the point-slope equation is (B) $f(x)=\frac{1}{2} x+6$.

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: $y-8=\frac{1}{2} (x-4)$

Distribute the right side:

$y-8=\frac{1}{2} (x)-\frac{1}{2} 4\\y-8=\frac{1}{2} x-2$

Adds 8 on both sides:

$y=\frac{1}{2}x-2+8\\y=\frac{1}{2}x+6$

Convert to function notation:

$f(x)=y\\f(x)=\frac{1}{2} x+6$

Therefore, the linear function which represents the line given by the point-slope equation is (B) $f(x)=\frac{1}{2} x+6$.

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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