Step by step
The question
Question: graph and remove t from x = 2t + 1, y = 2t − 3.
1 Make a table
Each t gives a point.
Start with t = −2.
x is 2 × (−2) + 1: −3.
y is 2 × (−2) − 3: −7.
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 = 2t + 1.
To remove + 1, we take away 1.
We do it on both sides, so they stay equal.
t has 2 in front.
To remove times 2, we divide by 2.
Put t into y = 2t − 3, with its bracket.
Careful!
2 multiplies all of t.
Keep the bracket, then open it.
2/2 is 1.
Open the bracket: 1 times x, and 1 times −1.
−1 minus 3 is −4.
So y = x − 4: a straight line.
5 Check
Let's check with a point from the table: t = 2 gave (5, 1).
Put x = 5 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.