Question

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

Answer 1

K for this, whenever a line is prependicular to another, the slope is the negative reciprocal. Negative Reciprocal means that the slope, -3/2 will turn into the reciprocal (opposite) -2/3, and the it'll switch signs, from negative to positive, or positive to negative. That means our slope is 2/3. Now we do point-slope formula again

y-y1=m(x-x1)

m=slope which is 2/3
and (x1,y1)= (3,9)
Now we pluck in the stuff in and solve :)

y-9=2/3(x-3) [First we distribute what's in parenthesis]
y-9=2/3x-2 [Now we add 9 to both sides]
y=2/3x+7 -> and that's our answer

-Hope that helps :)