Subjects algebra

Cartesian Equation E3Ca09

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1. The problem is to find the equation in Cartesian form. 2. Cartesian form means expressing the equation using $x$ and $y$ variables without parameters or other variables. 3. Since the problem does not specify the original form, let's assume a common parametric form: $x = f(t)$ and $y = g(t)$. 4. To convert to Cartesian form, solve one of the parametric equations for $t$ and substitute into the other. 5. For example, if $x = 2t + 3$ and $y = 4t - 1$, solve for $t$ from $x$: $$x = 2t + 3 \implies t = \frac{x - 3}{2}$$ 6. Substitute $t$ into $y$: $$y = 4\left(\frac{x - 3}{2}\right) - 1 = 2(x - 3) - 1 = 2x - 6 - 1 = 2x - 7$$ 7. The Cartesian form is $$y = 2x - 7$$ 8. This method applies generally: isolate $t$ from one equation and substitute into the other to eliminate $t$. 9. Without a specific parametric form given, this is the general approach to find Cartesian form.