Before we dig into the details, we can get a good idea of what the curve will look like by noting that both x and y have a simple relationship with t: they both increase linearly with it. Our final answer will be in the form of y = mx + b. So let's find that m and b.
Starting with x = 9t - 2, let's isolate t. Subtract t from both sides, giving us x - 2 = 9t. Divide both sides by 9, giving us (x - 2)/9 = t. We can rewrite that as x/9 - 2/9 = t, distributing the denominator.
Taking that x/9 - 2/9 = t, we have something that we can substitute into the y(t) equation. This gives us: y = 4(x/9 - 2/9) + 3. This quick substitution has delivered us an answer, since we have now eliminated t from the equation. But let's make it prettier. Distribute that 4 across the two terms, and we get y = 4x/9 - 8/9 + 3. Simplify by adding the like terms, and we get y = 4x/9 + 2 1/9, or y = 4x/9 + 19/9.
