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

Solution:

Given, point (2, -1/2)

Slope, m = 3

We have to find the equation of the line passing through the point with slope of 3.

The equation of a line passing through the point and slope of m is given by

\((y-y_{1})=m(x-x_{1})\)

Now, \((y-(-1/2))=3(x-2)\\(y+1/2)=3(x-2)\)

Therefore, the equation of the line is \((y+1/2)=3(x-2)\)

Which equation represents a line that passes through (2, -1/2) and has a slope of 3?

Summary:

The equation of a line that passes through (2, -1/2) and has a slope of 3 is \((y+1/2)=3(x-2)\).