Answer:
y = 2x/7 + 5
Explanation:
the first line is defined by
7x - 2y + 3 = 0
in the most common way to write this we need an equation like y = ...
so, we isolate the y-expression in the equation :
2y = 7x + 3
y = (7x + 3) / 2 = 7x/2 + 3/2
the factor of x is the slope of the line, which is expressed by the y/x ratio indicating how many units y will change, when x changes e.g. 1 unit.
7/2 means that y will change by 7 units for every change in x by 2 units.
the slope of a perpendicular line is inverse to the slope of the original line, which means x and y are simply trading places (original x / original y).
so, the perpendicular slope of 7/2 is 2/7 (when x changes by 7 units, then y changes by 2 units).
that means the equation for the perpendicular line is something like
y = 2x/7 + c
the c we determine by using the coordinates of the given point (x and y values).
3 = 2×(-7)/7 + c = 2×(-1) + c = -2 + c
c = 5
so, the complete equation of the perpendicular line is
y = 2x/7 + 5