Which of the following is the equation of a line perpendicular to the line, , passing through the point (3,9)?
y=-3/2x+4

a; 2x-3y=21
b; -2x+3y=21
c: -2x-3y=-21
d: 2x+3y=21

Y = -3/2x + 4...slope is -3/2
A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So that means the slope we will need is 2/3...see how I flipped the slope and changed the sign.
Now we use y = mx + bslope(m) = 2/3(3,9)...x = 3 and y = 9.
Time to sub...we r looking for b, the y intercept.

9 = 2/3(3) + b
9 = 2 + b
9 - 2 = b
7 = b 

so the perpendicular equation is : y = 2/3x + 7...but we need it in Ax + By = C form
y = 2/3x + 7multiply by common denominator of 3 to get rid of fractions
3y = 2x + 21...subtract 2x from both sides
-2x + 3y = 21<== ur answer...normally, I would have multiplied this by -1 to make x positive...but that is not an answer choice

What are the following algebraic equations. you need to post those if you want the answer

Distance=slopeslope is -2/4which equals-1/2the distance between these two points is -1/2