Intermediate Algebra 2e

# Key Terms

boundary line
The line with equation $Ax+By=CAx+By=C$ is the boundary line that separates the region where $Ax+By>CAx+By>C$ from the region where $Ax+By
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 $y=b.y=b.$ The line passes through the y-axis at $(0,b).(0,b).$
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 $Ax+By=C,Ax+By=C,$ 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≥C,Ax+ByC,Ax+By≥C,Ax+By or $Ax+By≤C,Ax+By≤C,$ 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, $(x,y)(x,y)$ 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 $(0,0)(0,0)$ 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 $(x1,y1)(x1,y1)$ is $y−y1=m(x−x1).y−y1=m(x−x1).$
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,$(x,y).(x,y).$ 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 $(x,y)(x,y)$ is a solution of the linear equation$Ax+By=C,Ax+By=C,$ 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 $(x,y)(x,y)$ 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 $Ax+By=C.Ax+By=C.$
vertical line
A vertical line is the graph of an equation of the form $x=a.x=a.$ The line passes through the x-axis at $(a,0).(a,0).$