Need help with these algebra questions?

Question

1.Write an equation in slope-intercept form for the line that is perpendicular to the line y = (-1/3)x + 4 that passes through the given point (-4,2). Pleas show work

2.Write an equation in slope-intercept form for the line that is parallel to the line y = -4x + 5 and that passes through the given point (-8,5).

pleas show work

Answer 1

1. gradient of the line= -1/3

    gradient of perpendicular= 3

  

   equation of the perpendicular

      y=mx+c

      y=3x+c

  now this line passes through the co-ordinates (-4,2) so you substitute the values

     (2)=3(-4)+c

      2=-12+c

       14=c



the equation is

y=3x+14

2. for a parallel line the gradient is going to be the same so

    m=-4

    

  equation of the parallel line is

  y= -4x+c



substitute the values of the co-ordinates

5= -4(-8)+c

5= 32 +c

-27=c

the equation of the parallel line is:

y= -4x-27

Answer 2

1)  y = (-1/3)x + 4 perpencicular to this means the slope is the negative reciprocal of -1/3 so the slope is 3

y = 3x + b, now you just have to find b if x = -4 and y = 2

2 = 3(-4) + b

2 = -12 + b

14 = b

the equation is y = y = 3x + 14

2)  Almost like the first one except if the line is parallel they have the same, so the slope is -4

y = -4x + b, find b if x = -8 and y = 5

5 = -4(-8) + b

5 = 32 + b

-27 = b

y = -4x - 27

Answer 3

First, slope-intercept form is y=mx+b. m= the slope

1) A perpendicular line has an opposite slope, therefore the slope is 3.

y - y1 = m(x - x1)

y - 2 = 3(x + 4)

y - 2 = 3x +12

y= 3x +14

2) A parallel line has the same slope, therefore the slope is -4

y - y1 = m(x - x1)

y - 5 = -4(x + 8)

y - 5 = -4x - 32

y= -4x -27

Both answers can be verified by using a graphing calculator.