Hi Cristina,
The general equation for a line is y = mx + b where m is the slope and b is the y intercept (where the line crosses the y axis). The slope of a line perpendicular to another line is the negative reciprocal. For example if the slope of one line is 2, then the slope of its perpendicular is -1/2.
So first you need to rewrite the given equation in the form above.
7x - 2y = -3
subtract 7x from each side:
-2y = -3 -7x
divide each side by 2:
-y = -3/2 -7x/2
multiply each side by -1:
y = 3/2 + 7x/2
rearrange the right side:
y = 7x/2 + 3/2
So the slope is 7/2 and its perpendicular slope is -2/7
Now we need to solve for b for the perpendicular line by plugging in the coordinates (X=21 and y =2):
y = mx +b
2 = (-2 x 21) +b
-------------
7
2 = -42/7 + b
2 = -6 +b
8 =b
So the equation of the perpendicular line is y = -2x/7 + 8
I would be happy to tutor you in math if you need the help.
Dan Lack
