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 right - hand side

Expand $\frac{1}{2}(x - 4)$ using the distributive property $a(b - c)=ab - ac$. Here $a=\frac{1}{2}$, $b = x$, $c = 4$. So $\frac{1}{2}(x - 4)=\frac{1}{2}x-2$. The equation becomes $y - 8=\frac{1}{2}x-2$.

Step2: Solve for $y$

Add 8 to both sides of the equation $y - 8=\frac{1}{2}x-2$. $y=\frac{1}{2}x-2 + 8$. $y=\frac{1}{2}x+6$. Since $y = f(x)$ in function notation, $f(x)=\frac{1}{2}x + 6$.

Answer:

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