### Geometry of Equations

Building blocks

Here are the equations of 12 straight lines.

$y=4x+4$

$4y=x+3$

$y=8x-3$

$y+4x+6=0$

$3y=2x-8$

$y+6x=11$

$y+8x=6$

$2y+8=3x$

$2y+x=4$

$2y=8x+3$

$y=6x-4$

$y+x+8=0$

These 12 straight lines can be divided up into six pairs, each pair matching one of the following descriptions:

• These lines are parallel.

• These lines are perpendicular.

• These lines have the same $y$-intercept.

• These lines have the same $x$-intercept.

• These lines both go through the point $(1,5)$.

• These lines …

Can you sort them into the correct pairs and complete the final description?

Note that the $x$-intercept of a line is where the line crosses the $x$-axis.

This resource is taken from the Standards Unit. You can download the full unit here, or just the printable card sorting pages (lines and descriptions) here.