501 Geometry Questions

Standard Form of Linear Equations

The first form that linear equations can be written in is called the standard form:

Standard Form of Linear Equations: Ax + By = C,

where A, B, and Care all numbers and x and yremain as variables.

To test if a given coordinate pair is on the a line that is in standard form,
simply plug the coordinates into the x and yvariables in the equation and
see if the result is true or false. For example, if you wanted to test to see if
the coordinate pairs (5,13) and (4,10) were on the line –6x+ 3y= 9, plug in
each point separately and see:

(5,13)

–6(5) + 3(13) = 9

–30 + 39 = 9

9 = 9

Since this is a true statement, (5,13) is a solution to –6x+ 3y= 9, and is
on that line.

(4,10)

–6(4) + 3(10) = 9

–24 + 30 = 9

6 ≠ 9

Since this is a false statement, (4,10) is not a solution to –6x+ 3y= 9,
because it is not on that line.
When using an equation to generate points that are on the line, it can be
easiest to isolate the xor yvariable in the equation. In the following exam-
ple, the equation –6x+ 3y= 9 is manipulated to get yon its own so that solu-
tions can easily be found:

–6x+ 3y= 9

+6x + 6x

3 y= (9 + 6x)

    3   3

y = 3 + 2x

501 Geometry Questions