geometry help please!?

Question

a. Write the equation of the line that is parallel to the line 2x-3y= 0 and contains the point (3,2).
b. Write the equation of a line that is perpendicular to the line 3x-y= -2 and contains the point (0,2).

Answer 1

Rewrite your expressions in the form y=mx+b, where m is the slope and b is the y-intercept (i.e., where x = 0).

a) 2x - 3y = 0
-3y = -2x
3y = 2x
y = 2/3 x

b) 3x - y = -2
3x = y - 2
y = 3x + 2

For a), two lines are PARALLEL if they have the same slope. So you need a line with slope 2/3 that passes through (3,2). You now have a y, your m, and an x...you just need to solve for b.
y = mx + b
2 = 2/3 (3) + b
2 = 2 + b
b = 0.
The line is y = 2/3x + 0. This is actually the line you are given, but I suppose it's parallel to itself.

For b), two lines are PERPENDICULAR if their slopes are negative reciprocals of each other. Since the slope of your line is 3, the slope of the perpendicular line is -1/3. With the point (0,2) on that line, you now have an x, your m, and a y.
y = mx + b
2 = (-1/3)(0) + b
2 = 0 + b
2 = b
So the perpendicular line is y = -1/3 x + 2.

Answer 2

1) the equation is 2x -3 y = 0 for the given point verfies that eq, and every line is parallel to itself
2) the equation is x+3y = c , subistituting the given point ( 0,2) in that eq. we get c = 6
So the eq, is : x + 3 y = 6

Answer 3

Hints: y = mx + b
Parallel lines have the same slope
A line perpindicular to y = mx + b has slope -1/m
Saying that the point (p,q) is contained in the line
y = mx + b is the same as saying q = mp + b

Now get off yer deadass and do your homework.


Doug

Answer 4

a.)
2x - 3y = 0
-3y = -2x
y = (2/3)x

(3,2), m = (2/3)

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

ANS : y = (2/3)x

-------------------------------

b.)
3x - y = -2
-y = -3x - 2
y = 3x + 2

(0,2), m = (-1/3)
2 = (-1/3)(0) + b
2 = 0 + b
b = 2

ANS : y = (-1/3)x + 2

Answer 5

a. 2x-6y=0
b. x-3y=-2


Hope This Helps