Help, please!!? I don't understand these problems.?

Question

I really can't figure out how to do these problems, any help is appreciated!

1) perpendicular to the line y= 1/2x + 4 and contains the point (1,-2)

2) perpendicular to the line 2x+y=2 and contains the point (-3,0)

3) perpendicular to the line x=8 and contains the point (3,4)

They are just so confusing!

Answer 1

Find the slope of the line.  The slope of the perpendicular line is the negative reciprocal of the slope of the line.

if m =a/b then m perp = - b/a

plug the point and m perp into y = mx + b and solve for b.  Then you have your equation.

Answer 2

you need to know that the general form of a line is  



y=mx+b                               m is the slope

when you have perpendicular lines, that means the slope of the line is -1/2 times the other one...

and in your examples, find the m (slope),   then multiply that by  - 1/2 to get the slope of the perpendicular line's slope.

now you need the b.

you plug in the point provided (x, y) to solve for c

in your first example:

y = 1/2 x + 4          this means the perpendicular slope is -2

so new equation is:    y=-2x+ b  

plug in the points (1, -2)

                       -2 = -2(1) + b

                      -2  = -2 +b

                     0  =  b

so the equation of your line that ocntains the point (1, -2) in your example 1, is   y = - 2x

good luck

Answer 3

1) perpendicular to the line y= 1/2x + 4 and contains the point (1,-2)

We'll need to use the formula: y-y(sub 1) = M(x-x(sub 1))

And the formula: y = Mx+b

Where M is the slope of the line, and b is the y-intercept.

For the line y = 1/2x + 4, the slope is obviously 1/2

So we say that M=1/2, but we want the line that is perpendicular so we make it M=-2 (the negative reciprocal)

Now we use the first formula with the perpendicular slope:

y - (-2) = -2(x - 1)

y + 2 = -2x + 2

y = -2x + 2 - 2

y = -2x

And this is the equation you are seeking!

Now, using the above, are you able to figure the other two out? If not feel free to email me and I'll give some more help.

Have a good day!