The general form of a linear equation is
y = mx + b
where m = slope and b = y-intercept
Here m = 2/7
To get to its perpendicular equation, first the slope should be negative reciprocal. So the perpendicular slope is m = -7/2
Given the point (-2,3), use the point-slope form equation, that is
y - y1 = m(x - x1)
Plug in
y - 3 = (-7/2)[x - (-2)]
y - 3 = (-7/2)x - 7
y = (-7/2)x - 7 + 3
y = (-7/2)x - 4
That is the equation required.