If we sub the t values of -1, 0, 1, 2, 3, 4 into the equation for x, we have x values of 2, 3, 4, 5, 6, 7. If we plug those t values into the equation for y, we have y values of -2, 0, 2, 4, 6, 8. When we put those together in coordinate form we have (2, -2), (3, 0), (4, 2), (5, 4), (6, 6), (7, 8). If you plot those points on a piece of graph paper they form a straight line. So in order to write the equation of that line, we need the slope between any 2 points. Let's pick the second and third points (no negatives!) and fit them into the slope formula:
. So the slope is 2. Now we will use a point, an easy one (let's use the second one) and fill in the point-slope formula like so:
y - 0 = 2(x - 3) and distribute to get y - 0 = 2x - 6 or simplifying, y = 2x - 6. That's the equation you want in rectangular form.