Do you think this answer correct?

Question

Find the equation of the line that satisfies the following information. Perpendicular to the line 2x + 3y = 12 passing thru the origin.

2x + 3y = 12

-------------------
3y = -2x + 12


y = (-2/3)x + 4

slope is -2/3

the equation of line perpendicular to the first one is

answer : y = (3/2)x + b?

Thanks.

Answer 1

Looks correct to me - the negative reciprocal of the original slope.

And if it passes through the origin (0,0), then the b in your equation would also equal 0.

Plug in y=0 and x=0 to your equation

0=(3/2)*0 + b ====> b=0

Final equation: y=(3/2)x

Answer 2

you would sub x and y in to get b and if the line passes throudh the origin then x and y both equal 0 so the equation turns into 0=3/2(0)+b so you multiply the slope and x to get 0 then you get 0=b so the equation of the line perpendicular to y= -2/3x+4 is y=3/2x

Answer 3

To find the equation of a line that is perpendicular to another, you must consider the vectors of the lines are perpendicular.
So a possible vector of the original equation is (-3;2). Note nevertheless that such a line has an infinity of vectors.
You must then consider that the vectors of the other line will be perpendicular to the vectors of the initial one.
Let's say the vector we'll consider in the perpendicular line has the coordinates (x;y)
The dots verifying this Cartesian product:
(x;y).(-3;2)=0
Will be the equation of the line:
-3x+2y=0
The equation of this line shows it passes by the origin. The image of zero is zero.
You couldn't decide the equation would pass by the origin, my friend. Things are just that way.

Answer 4

yes, but you have to define b. You can easily set be the same as the b for the first equation. So, y=(3/2)x+4.

Answer 5

you were correct up to y= -2/3y + 4

after that, it depends on exactly how the question was worded or what you are solving. The equation is not necessarily a slope, but i guess your doing something with slopes.

Answer 6

yeh, that's right