Step by step
The question
Question: graph and remove t from x = t + 2, y = t − 1.
1 Make a table
Each t gives a point.
Start with t = −2.
x is (−2) + 2: 0.
y is (−2) − 1: −3.
Put the t's in a table.
Work out x for each t,
and y for each t.
2 Plot the points
Draw the grid.
Put each (x, y) on the grid.
3 Join in order of t
Join the points in order: t = −2, then −1, and on.
The arrows show the way t grows.
t can go on, so the curve goes on.
4 Remove t
To get t alone, start with x = t + 2.
To remove + 2, we take away 2.
We do it on both sides, so they stay equal.
So t = x − 2.
Put t into y = t − 1, with its bracket.
Careful!
1 multiplies all of t.
Keep the bracket, then open it.
Open the bracket: 1 times x, and 1 times −2.
−2 minus 1 is −3.
So y = x − 3: a straight line.
5 Check
Let's check with a point from the table: t = 2 gave (4, 1).
Put x = 4 into the answer.
We get y = 1, the same as the table.
Right!
Let's look back.
First: make a table.
Then: plot the points.
Then: join in order of t.
Then: remove t.
Last: check.