The Cartesian plane and plotting lines

Coordinates in four quadrants, tables of values from a rule, plotting straight lines and checking whether a point lies on a line.

The Cartesian plane

A point $(x, y)$ is found by moving $x$ across, then $y$ up. The axes split the plane into four quadrants, numbered anticlockwise from the top right.

Coordinates and quadrants

Drag the point and watch its coordinates and quadrant.

Tables of values

Example 1●

Complete a table for $y = 2x - 1$ with $x = -1, 0, 1, 2$.

$y = -3, -1, 1, 3$

Plot $(-1, -3), (0, -1), (1, 1), (2, 3)$ and join them with a ruler.

Example 2●●

Does $(3, 5)$ lie on $y = 2x - 1$?

$2(3) - 1 = 5$ ✓, so yes.

Flashcards

Quadrant 2

$x$ negative, $y$ positive

The origin

$(0, 0)$

Is a point on a line?

Substitute $x$ and check you get $y$.

Practice

Which quadrant contains $(-3, 2)$?
For $y = 2x - 1$, find $y$ when $x = -1$.
Does $(3, 5)$ lie on $y = 2x - 1$?
Does $(2, 1)$ lie on $y = 3x - 4$?
Which quadrant contains $(4, -1)$?
For $y = 10 - x$, find $y$ when $x = 3$.
$(a, 4)$ lies on $y = -2x$. Find $a$.
Points on the $y$-axis always have: