Question

The equation of line WX is y = -2x - 5. Write an equation of a line perpendicular to line WX in slope-intercept form that contains point (-1, -2)

Answer 1

So perpendicular lines have opposite reciprocal slopes. Opposite meaning you multiply by -1, reciprocal meaning you take the inverse.

For example if your slope was 2, the perpendicular slope would be -1*1/(2)

In a more general case, a slope m would result in a perpendicular slope of -1/m

In your case the slope is -2x. The opposite reciprocal of -2x is -1*1/(-2) = -1/-2 = 1/2

We now know the slope, and we just need to solve for the y intercept to finish our equation.

Using the equation form y = mx + b and our given (that the line must cross through -1,-2), we now have a y value (y=-2), an x value (x=-1) and a slope (m=1/2). All we need to do now is solve for the y intercept.

-2 = 1/2*-1 + b
-2 = -1/2 + b
-3/2 = b

now just throw everything back into the equation and you're good to go!