# Key Terms Chapter 03: Graphs and Functions

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Example and Directions
Words (or words that have the same definition)The definition is case sensitive(Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages](Optional) Caption for Image(Optional) External or Internal Link(Optional) Source for Definition
(Eg. "Genetic, Hereditary, DNA ...")(Eg. "Relating to genes or heredity")The infamous double helix https://bio.libretexts.org/CC-BY-SA; Delmar Larsen
Glossary Entries
boundary lineThe 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 relationThe domain of a relation is all the $$x$$-values in the ordered pairs of the relation.
functionA function is a relation that assigns to each element in its domain exactly one element in the range.
horizontal lineA horizontal line is the graph of an equation of the form $$y=b$$. The line passes through the y-axis at $$(0,b)$$.
intercepts of a lineThe points where a line crosses the $$x$$-axis and the $$y$$-axis are called the intercepts of the line.
linear equationAn equation of the form $$Ax+By=C$$, where $$A$$ and $$B$$ are not both zero, is called a linear equation in two variables.
linear inequalityA linear inequality is an inequality that can be written in one of the following forms: $$Ax+By>C$$, $$Ax+By≥C$$, $$Ax+By<C$$, or $$Ax+By≤C$$, where $$A$$ and $$B$$ are not both zero.
mappingA 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 pairAn ordered pair, $$(x,y)$$ 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.
originThe point $$(0,0)$$ is called the origin. It is the point where the $$x$$-axis and $$y$$-axis intersect.
parallel linesParallel lines are lines in the same plane that do not intersect.
perpendicular linesPerpendicular lines are lines in the same plane that form a right angle.
point-slope formThe point-slope form of an equation of a line with slope $$m$$ and containing the point $$(x_1,y_1)$$ is $$y−y_1=m(x−x_1)$$.
range of a relationThe range of a relation is all the $$y$$-values in the ordered pairs of the relation.
relationA relation is any set of ordered pairs, $$(x,y)$$. 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 variablesAn ordered pair $$(x,y)$$ 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 inequalityAn ordered pair $$(x,y)$$ 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 equationA linear equation is in standard form when it is written $$Ax+By=C$$.
vertical lineA vertical line is the graph of an equation of the form $$x=a$$. The line passes through the $$x$$-axis at $$(𝑎,0)$$.