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

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

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

Answer

Answer:

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

Explanation:

Step1: Recall 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 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 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 $y+\frac{1}{2}=3(x - 2)$.