### Key Terms

- boundary line
- The line with equation $Ax+By=C$ is the boundary line that separates the region where $Ax+By>C$ from the region where $Ax+By<C.$

- domain of a relation
- The domain of a relation is all the
*x*-values in the ordered pairs of the relation.

- function
- A function is a relation that assigns to each element in its domain exactly one element in the range.

- horizontal line
- A horizontal line is the graph of an equation of the form $y=b.$ The line passes through the
*y*-axis at $\left(0,b\right).$

- intercepts of a line
- The points where a line crosses the
*x*-axis and the*y*-axis are called the intercepts of the line.

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

- linear inequality
- A linear inequality is an inequality that can be written in one of the following forms: $Ax+By>C,\phantom{\rule{0.4em}{0ex}}Ax+By\xe2\u2030\yen C,\phantom{\rule{0.4em}{0ex}}Ax+By<C,$ or $Ax+By\xe2\u2030\xa4C,$ where
*A*and*B*are not both zero.

- mapping
- A mapping is sometimes used to show a relation. The arrows show the pairing of the elements of the domain with the elements of the range.

- ordered pair
- An ordered pair, $\left(x,y\right)$ gives the coordinates of a point in a rectangular coordinate system. The first number is the
*x*-coordinate. The second number is the*y*-coordinate.

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

- parallel lines
- Parallel lines are lines in the same plane that do not intersect.

- perpendicular lines
- Perpendicular lines are lines in the same plane that form a right angle.

- point-slope form
- The point-slope form of an equation of a line with slope
*m*and containing the point $\left({x}_{1},{y}_{1}\right)$ is $y\xe2\u02c6\u2019{y}_{1}=m\left(x\xe2\u02c6\u2019{x}_{1}\right).$

- range of a relation
- The range of a relation is all the
*y-*values in the ordered pairs of the relation.

- relation
- A relation is any set of ordered pairs,$\left(x,y\right).$ All the
*x*-values in the ordered pairs together make up the domain. All the*y*-values in the ordered pairs together make up the range.

- solution of a linear equation in two variables
- 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.

- solution to a linear inequality
- An ordered pair $\left(x,y\right)$ is a solution to a linear inequality if the inequality is true when we substitute the values of
*x*and*y*.

- standard form of a linear equation
- A linear equation is in standard form when it is written $Ax+By=C.$

- vertical line
- A vertical line is the graph of an equation of the form $x=a.$ The line passes through the
*x*-axis at $\left(a,0\right).$