Step by step
The question
Question: graph and remove t from x = t, y = t + 3.
x = t and y = t + 3
1 Make a table
Each t gives a point.
Start with t = −2.
x is (−2): −2.
t = −2: x = (−2) = −2
y is (−2) + 3: 1.
y = (−2) + 3 = 1
Put the t's in a table.
Work out x for each t,
−2
−1
0
1
2
and y for each t.
1
2
3
4
5
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
So t = x.
t = x
Put t into y = t + 3, with its bracket.
y = x + 3
Careful!
1 multiplies all of t.
Keep the bracket, then open it.
Careful: not y = x + 3 ✗
So y = x + 3: a straight line.
y = x + 3
5 Check
Let's check with a point from the table: t = 2 gave (2, 5).
Put x = 2 into the answer.
We get y = 5, the same as the table.
Right!
x = 2: y = 2 + 3 = 5
Let's look back.
First: make a table.
Then: plot the points.
Then: join in order of t.
Then: remove t.
Last: check.
Answer
y = x + 3