which equation represents a line that passes through (2, -1/2) and has a slope of 3?\no y - 2 = 3(x +…

Explanation:

Step1: Recall point - slope formula

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Identify values of $x_1$, $y_1$ and $m$

Given the point $(2,-\frac{1}{2})$ and slope $m = 3$, so $x_1=2$, $y_1=-\frac{1}{2}$.

Step3: Substitute values into formula

Substitute $x_1 = 2$, $y_1=-\frac{1}{2}$ and $m = 3$ into $y - y_1=m(x - x_1)$, we get $y-(-\frac{1}{2})=3(x - 2)$, which simplifies to $y+\frac{1}{2}=3(x - 2)$.

Answer:

C. $y+\frac{1}{2}=3(x - 2)$