Which of the following is the equation of a line perpendicular to the line y=-3/2x+4, passing through the point (3, 9)? 2x+3y=21 2x-3y=21 -2x+3y=21 -2x-3y=-21

-2x+3y = 21 which is choice C

Work Shown:

The slope of the original line is -3/2. The perpendicular slope is 2/3. We flip the fraction and flip the sign. Multiplying the original slope (-3/2) and the perpendicular slope (2/3) will result in -1. Let's use this perpendicular slope and the point to find the equation of the perpendicular line in slope intercept form.

y = m+b

y = (2/3)x+b plug in the perpendicular slope

9 = (2/3)(3)+b plug in the point (x,y) = (3,9)

9 = 2+b

9-2 = 2+b-2 ... subtract 2 from both sides

b = 7

So y = (2/3)x+b turns into y = (2/3)x+7.

This equation is in slope intercept form.

Let's convert to standard form

y = (2/3)x+7

3*y = 3*((2/3)x+7) ... multiply both sides by 3 to clear out the fraction

3*y = 3*(2/3)x+3*7 ... distribute

3y = 2x+21

-2x+3y = 21 get the x term to the other side (subtract 2x from both sides)

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted