Question

Determine the equation of the line that passes through the point (-1, 2) and isperpendicular to the line y = -2.

Answer 1

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

1) In this question, let's find the equation, using the point-slope formula:

`(y-y_0)=m(x-x_0)`

2) Notice that since we want a perpendicular line we can write a perpendicular line to y=2, as x=-1/2 for -1/2 is the opposite and reciprocal to 2 (the necessary condition to get a perpendicular line).

So, the slope of that perpendicular line is -1/2

3) Let's plug into that Point-Slope formula, the slope m= -1/2 and the point:

`\begin{gathered} (y-2)=-(1)/(2)(x+1) \\ y-2=-(1)/(2)x-(1)/(2) \\ y=-(1)/(2)x-(1)/(2)+2 \\ y=-(1)/(2)x+(3)/(2) \end{gathered}`

4) Thus, the answer is:

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