which linear function represents the line given by the point - slope equation $y - 8=\frac{1}{2}(x…

which linear function represents the line given by the point - slope equation $y - 8=\frac{1}{2}(x - 4)$?\n$\\bigcirc$ $f(x)=\frac{1}{2}x + 4$\n$\\bigcirc$ $f(x)=\frac{1}{2}x + 6$\n$\\bigcirc$ $f(x)=\frac{1}{2}x - 10$\n$\\bigcirc$ $f(x)=\frac{1}{2}x - 12$

which linear function represents the line given by the point - slope equation $y - 8=\frac{1}{2}(x - 4)$?\n$\\bigcirc$ $f(x)=\frac{1}{2}x + 4$\n$\\bigcirc$ $f(x)=\frac{1}{2}x + 6$\n$\\bigcirc$ $f(x)=\frac{1}{2}x - 10$\n$\\bigcirc$ $f(x)=\frac{1}{2}x - 12$

Answer

Explanation:

Step1: Expand the point - slope form

We have the point - slope equation (y - 8=\frac{1}{2}(x - 4)). Using the distributive property (a(b - c)=ab - ac), where (a = \frac{1}{2}), (b=x) and (c = 4), we get (y-8=\frac{1}{2}x-\frac{1}{2}\times4). Since (\frac{1}{2}\times4 = 2), the equation becomes (y - 8=\frac{1}{2}x-2).

Step2: Solve for y (or f(x))

To isolate (y), we add 8 to both sides of the equation. So (y=\frac{1}{2}x-2 + 8). Combining like terms (-2+8 = 6), we have (y=\frac{1}{2}x + 6). In function notation, (f(x)=\frac{1}{2}x+6).

Answer:

(f(x)=\frac{1}{2}x + 6) (the second option: (f(x)=\frac{1}{2}x+6))