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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).

Verified Answer :

 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

Panoyin
  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

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