To eliminate the parameter from the equations involving variables such as x, y, and t, we first start by understanding how these expressions relate to each other. In this specific case, the expression x = 5t and y = t + 8 defines a relationship where y depends on t and x is also defined based on t.
Firstly, we’ll solve one of the parameter equations for ‘t’. We can take the equation for x:
- x = 5t
From this, we can express t in terms of x:
- t = x / 5
Next, we substitute this expression of t into the second expression for y:
- y = t + 8
Substituting for t gives us:
- y = (x / 5) + 8
This equation represents y as a function of x. Now we have effectively eliminated the parameter t from the equations, and our final expression is:
- y = (x / 5) + 8
This step brings us to a linear relationship between x and y. The graph of this equation would be a straight line where, for every change in x, y will respond accordingly based on the equation defined.
In summary, by expressing the parameter t in terms of x and substituting it back into the equation for y, we have eliminated the parameter, leading us to a relationship directly linking x and y without any parameters left in the equation.