Question

Find an equation of the line that satisfies the given conditions.

Through (−1, −2); perpendicular to the line 2x + 7y + 2 = 0

Answer 1

remember, we talked about "slope form" of the equation...?
we need that one now.
re-write your equation in slope form:
7y=-2x-2
y=-2/7 x -2/7
the coefficient in a front of x is a slope:
m=-2/7

Answer 2

now you need a line perpendicular to that one, which means the slope of YOUR line will be:
m1= 7/2 (m=-1/m)
now you know the slope of your desired line and your know the point that it has to go through, then:
y-(-2)=7/2 (x-(-1))
y+2=7/2 (x+1)
y=7/2 x +7/2 -2
y=7/2 x +3/2
this is the equation of your line