Key Concepts

Key Concepts

• Sign Patterns of the Quadrants
  \(\begin{array}{cccccccccc}\text{Quadrant I}\hfill & & & \text{Quadrant II}\hfill & & & \text{Quadrant III}\hfill & & & \text{Quadrant IV}\hfill \\ \left(x,y\right)\hfill & & & \left(x,y\right)\hfill & & & \left(x,y\right)\hfill & & & \left(x,y\right)\hfill \\ \left(+,+\right)\hfill & & & \left(\text{−},+\right)\hfill & & & \left(\text{−},\text{−}\right)\hfill & & & \left(+,\text{−}\right)\hfill \end{array}\)
• Points on the Axes
  
  • On the x-axis, \(y=0\). Points with a y-coordinate equal to 0 are on the x-axis, and have coordinates \(\left(a,0\right)\).
  • On the y-axis, \(x=0\). Points with an x-coordinate equal to 0 are on the y-axis, and have coordinates \(\left(0,b\right).\)
• Solution of a Linear Equation
  
  • An ordered pair \(\left(x,y\right)\) is a solution of the linear equation \(Ax+By=C\), if the equation is a true statement when the x- and y- values of the ordered pair are substituted into the equation.

Glossary

linear equation

A linear equation is of the form $Ax+By=C$, where A and B are not both zero, is called a linear equation in two variables.

ordered pair

An ordered pair $(x,y)$ gives the coordinates of a point in a rectangular coordinate system.

origin

The point $(0,0)$ is called the origin. It is the point where the x-axis and y-axis intersect.

quadrant

The $x$-axis and the $y$-axis divide a plane into four regions, called quadrants.

rectangular coordinate system

A grid system is used in algebra to show a relationship between two variables; also called the $xy$-plane or the ‘coordinate plane’.

$x$-coordinate

The first number in an ordered pair $(x,y)$.

$y$-coordinate

The second number in an ordered pair $(x,y)$.