find the value of c for which the line 3x+cy=5
(c) is parallel to the line 2x+y=-1
(d) has equal x and y-intercepts
(e) is perpendicular to the line y-2=3(x+3)

Question

anonymous · Answer

a) replace $x$ by $3$ and $y$ by 1 
solve $3\times 3+c\times 1=5$ for $c$

anonymous · Answer

To find the answer to a, plug the x coordinate (3) in to x and the y coordinate (1) in to y. So 3(3)+c(1)=5. Then solve for c. 9+c=5, 9-9+c=5-9, c=-4. 
For b, plug 0 in for x in the equation. 3(0)+cy=5, cy=5, c=y/5. I know that looks like a weird answer, and I'm not 100% sure it's right, but it's the best I can do with three variables.
Parallel lines have the same slope, so the best way to do c is rearrange both of those into slope-intercept form. The first one becomes (cy=5-3x, y=(5-3x)/c) and the second becomes (y=-1-2x). The slope of the first is (-3x/c) and the second is (-2x). To find the c for which this works, set them equal to each other and solve. (-3x/c=-2x, -3x/c*c=-2x*c, -3x=-2xc, -3x/-2x=-2xc/-2x, 3/2=c).
Any other helpers that might read through this, one of you guys help him (or her) with d and e. I'm not so great at those.

anonymous · Answer

tnx singlesixx and satellite73

phi · Answer

(b) is parallel to the y-axis
a line parallel to the y-axis has an undefined slope.  if we re-write
 3x+cy=5

as     y=  (-3/c) x + 5/c
we can make the number in front of the x (which will be the slope) undefined by dividing by 0.  In other words, let c=0

another (maybe better) way is to know that a line parallel to the y-axis  has no y in its equation
so if we change 3x+c y = 5  to 3x =5   or x= 5/3  we get a line parallel to the y-axis
to do this, we have to set c=0 to make the c*y part "go away"

anonymous · Answer

b is correct phi,tnx pls what about c,d & e?

phi · Answer

to do (c) is parallel to the line 2x+y=-1

you first have to figure out the slope of 
2x+y=-1

to find the slope, you have to "solve for y"
can you do  that ?

phi · Answer

"solve for y" means getting the y by itself on the left side of the = sign.

anonymous · Answer

y=-2x+1 is that?

anonymous · Answer

not very sure

phi · Answer

close
you start with
2x+y=-1

you want to y by itself.  if you add -2x to both sides you get
-2x+2x+y= -2x -1
the -2x+2x is 0    and 0 +y is y   so the left side is
y= -2x -1
you were close

what is the slope of y= -2x -1 ?

phi · Answer

the reason we write it in the form y= mx + b
is because m (the number in front of the x) is the slope.

anonymous · Answer

and what is C?