Which of these is perpendicular?

get all into slope-intercept form

a) y = –(2/3)x + 7

b) y = +(2/3)x + 7

c) y = –(2/3)x + 7

d) y = –(2/3)x + 7

to be perpendicular to y = –(3/2)x + 4 

the line would have a slope of +(2/3) which is (b)

does it pass thru 3,9 ?

y = +(2/3)x + 7

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

yes

 The following is the equation of the line perpendicular to the line

 y = -3/2x + 4  

 y = 1/2 (8 - 3 x)  9 = -9/2

 passing through the point (3, 9)

 a) 2x + 3y = 21

 b) -2x + 3y = 21

 c ) 2x - 3y= 21             ✔

 d ) -2x - 3y = -21

Perpendicular lines have negative-reciprocal slopes.

The slope of the given line is -3/2 so the slope of any perpendicular line is 2/3.

We are given a point to give us x and y.  We can solve for the unknown intercept:

y = mx + b

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

9 = 2 + b

7 = b

Now the equation in slope-intercept form is:

y = (2/3)x + 7

To put this into standard form, subtract the "x" term from both sides, multiply both sides by the denominator, then make sure the coefficient of the x term is positive:

-(2/3)x + y = 7

-2x + 3y = 21

Since it's negative, we multiply both sides by -1:

2x - 3y = -21

None of the answers match this.  So if we go with almost-standard form and go with the negative value in x's coefficient, that matches option B.  But again, that's not proper standard form.