How do you write the corresponding rectangular equation by eliminating the parameter given x = 3 t − 1 , y = 2 t + 1?

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How do you write the corresponding rectangular equation by eliminating the parameter given   x  =  3  t  −  1  ,  y  =  2  t  +  1?

lutzantsca885 · Accepted Answer

Step 1t is a parameter for       x    =    x          (      t      )       and       y    =    y          (      t      , and in this example it appears once in a linear form, so we can rewrite each equation as:      x    =    3    t    -    1    ⇒    t    =          1      3              (      x      +      1      )            y    =    2    t    +    1    ⇒    t    =          1      2              (      y      -      1      )      Step 2And then as t is the common parameter we can equate these expressions to give:            1      2              (      y      -      1      )        =          1      3              (      x      +      1      )      Then it is just a case of re-arranging this equation until we get       y    =    y          (      x      )            3          (      y      -      1      )        =    2          (      x      +      1      )            ∴    3    y    -    3    =    2    x    +    1        ∴    3    y    =    2    x    +    4        ∴    y    =          2      3        x    +          4      3

How do you write the corresponding rectangular equation by eliminating

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