Eliminating the parameter in the parametric equations x = 5 − 3 t , y = 2 + t yields what equation?

Question

Eliminating the parameter in the parametric equations   x  =  5  −  3  t  ,     y  =  2  +  t yields what equation?

Hayley Mccarthy · Accepted Answer

Step 1Because t is linear in both expressions we can easily eliminate the parameter as follows:      x    =    5    -    3    t        ∴    3    t    =    5    -    x        ∴    t    =                  5        -        x            3            y    =    2    +    t        t    =    y    -    2  As t is the common parameter these two expressions are identical; thus;      t    =                  5        -        x            3        =    y    -    2        y    -    2    =          5      3        -          x      3            y    =    -          x      3        +          11      3      Which is a straight line with gradient       -          1      3       and y-intercept             11      3

Eliminating the parameter in the parametric equations x

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