which equation represents a line that passes through (2, -1/2) and has a slope of 3?\n○ y - 2 = 3(x +…

Explanation:

Step1: Recall the point - slope form

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 the values of (x_1,y_1) and (m)

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

Step3: Substitute into the point - slope form

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:

(y+\frac{1}{2}=3(x - 2)) (the third option)