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: $Ax+By>C,Ax+By\ge C,Ax+By<C,$ or $Ax+By\le C,$ 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 $y-y_1=m\left(x-x_1\right).$

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 $\left(a,0\right).$