Question

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

O y-2 = 3(x +1/2)
O y-3 = 2(x + 1/2)
O y+ 1/2 = 3(x - 2)
o y + 1/2 = 2(x - 3)

Answer 1

`\displaystyle y + (1)/(2) = 3\, (x - 2)`.

Explanation:

Consider a line in a cartesian plane that goes through the point
`(x_(0),\, y_(0))`. If the slope of this line is
`m` (a real constant,) the equation of this line in point-slope form would be:

`y - y_(0) = m\, (x - x_(0))`.

The line in this question goes through the point
`(2,\, (-1/2))`. Thus,
`x_(0) = 2` whereas
`y = (-1/2)`. The slope of this line is
`m = 3`. Thus, the equation of this line in point-slope form would be:

`y - (-1/2) = 3\, (x - 2)`.

Simplify to obtain:

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