I need help with 2 math problems?

Question

Write the standard form of the equation of the line parallel to the graph of x - 2y - 6 =0 and passing through C(0,1)

also...

Write an equation of the line perpendicular to the graph of x=3 and passing through D(4, -1)

A. x - 4 =0

B. x + 1 =0

C. y + 1 =0

D. y - 4 =0

Answer 1

From x-2y-6=0,-2y=-x+6

2y= x-6

y=(1/2)x-6

The slope of our line y=mx+b is 1/2, because it is parallel to the given line.

Our line so far looks like this:

y=(1/2)x+b

Our line passes through (0,1)

Therefore 1=(1/2)0+b

b=1

Our equation is y =(1/2)x+1

In standard form this is  2y=x+2, or

-x+2y-2=0, and finally

x-2y+2=0

x=3 is a line parallel to the y-axis and 3 unite to the right of it.

The perpendicular line you seek is therefore going to be a line parallel

to the x-axis. Since it passes through (4,-1), the equation is going to

be y= -1, or y+1=0

Answer 2

a) slope is 1/2

the equation is y-1=[1/2][x-0]

==>2y-2=x

b) perpendicular is y=-1

   so, the answer is C

Answer 3

If they are parallel then it has the form x - 2y + c = 0. Substitute (0,1) in to find c: 0 - 2 + c = 0 => c=2

Perpendicular to x=3 means it is of the form y=c. Passing through (4, -1) gives us c = -1.

Answer 4

1. y = 1/2x - 3

2. C

Answer 5

this reminds me of my math homework!

Answer 6

The slope of the line in the first question is:  1/2

Can you get that?

The y-intercept of the parallel line is point C!

So, the equation, in slope-intercept form, is:  y = (1/2)x + 1

Can you put this equation in standard form?

Question 2 involves perpendicular lines.  What kind of line is x = 3?

Draw it on some axes.  Does it go from side to side (horizontal) or does it go up and down (vertical) ?

Draw a line perpendicular to x = 3

Make it go through (4, -1)

Hmmm... how does it go?

y = -1, or y + 1 = 0