1.) write the equation of the line perpendicular to the line x - 5y = -10 and passing through the point (2,5).

2.) write the equation of the line parallel to the line 10x - 5y = 8 and passing through the point (2,4).

3.) write the equation of the line parallel to the line 4x + y = -1 and passing through the point (5,0).

4.) write the equation of the line parallel to the line 4x + 2y = 5 and passing through the point (-3,5).

5.) write the equation of the line perpendicular to the line x - 3y = 9 and passing through the point (3,5).

 write the equation in y = mx + b.
5Y = -10-x
y=-2-x/5
y=-1/5x-2
the slope = -1/5

 put new slope from step 3 and a point into y = mx + b to find b.
5 = (2)(-1/5) + b
5=-2/5+b
5+2/5=b
25+2/5=b
27/5=b
13.5=b
Y = -1/5+13.5

1. x - 5y = -10
  - x            - x
        -5y = -x - 10
         -5        -5
           y = ¹/₅x + 2

     y - y₁ = m(x - x₁)
      y - 5 = -5(x - 2)
      y - 5 = -5(x) + 5(2)
      y - 5 = -5x + 10
        + 5           + 5
           y = -5x + 15

2. 10x - 5y = 8
  - 10x        - 10x
            -5y = -10x + 8
             -5          -5
                y = 2x - 1³/₅

          y - y₁ = m(x - x₁)
           y - 4 = 2(x - 2)
           y - 4 = 2(x) - 2(2)
           y - 2 = 2x - 4
             + 2        + 2
                y = 2x - 2

3. 4x + y = -1
  - 4x          -4x
           y = -4x - 1

     y - y₁ = m(x - x₁)
      y - 0 = -4(x - 5)
      y - 0 = -4(x) + 4(5)
      y - 0 = -4x + 20
        + 0          + 0
           y = -4x + 20

4. 4x + 2y = 5
  - 4x          - 4x
           2y = -4x + 5
            2          2
             y = -2x + 2¹/₂

       y - y₁ = m(x - x₁)
        y - 5 = -2[x - (-3)]
        y - 5 = -2(x + 3)
        y - 5 = -2(x) - 2(3)
        y - 5 = -2x - 6
          + 5         + 5
             y = -2x + 1

5. x - 3y = 9
  - x         - x
        -3y = -x + 9
         -3        -3
           y = ¹/₃x - 3

     y - y₁ = m(x - x₁)
      y - 5 = -3(x - 3)
      y - 5 = -3(x) + 3(3)
      y - 5 = -3x + 9
        + 5          + 5
           y = -3x + 14