Step by step
The question
Question: graph and remove t from x = t − 1, y = 2t + 1, for 0 ≤ t ≤ 3.
1 Make a table
Each t gives a point.
Start with t = 0.
x is 0 − 1: −1.
y is 2 × 0 + 1: 1.
Put the t's in a table: t from 0 to 3.
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 = 0, then 1, and on.
The arrows show the way t grows.
4 Remove t
To get t alone, start with x = t − 1.
To remove − 1, we add 1.
We do it on both sides, so they stay equal.
So t = x + 1.
Put t into y = 2t + 1, with its bracket.
Careful!
2 multiplies all of t.
Keep the bracket, then open it.
Open the bracket: 2 times x, and 2 times 1.
2 plus 1 is 3.
So y = 2x + 3: a straight line.
5 Check
Let's check with a point from the table: t = 3 gave (2, 7).
Put x = 2 into the answer.
We get y = 7, 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.