Elementary Algebra 2e

# Key Terms

### Key Terms

boundary line
The line with equation $Ax+By=CAx+By=C$ that separates the region where $Ax+By>CAx+By>C$ from the region where $Ax+By.
geoboard
A geoboard is a board with a grid of pegs on it.
graph of a linear equation
The graph of a linear equation $Ax+By=CAx+By=C$ is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.
horizontal line
A horizontal line is the graph of an equation of the form $y=by=b$. 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
A linear equation is of the form $Ax+By=CAx+By=C$, where A and B are not both zero, is called a linear equation in two variables.
linear inequality
An inequality that can be written in one of the following forms:
$Ax+By>CAx+By≥CAx+ByCAx+By≥CAx+By

where $AandBAandB$ are not both zero.
negative slope
A negative slope of a line goes down as you read from left to right.
ordered pair
An ordered pair $(x,y)(x,y)$ gives the coordinates of a point in a rectangular coordinate system.
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
Lines in the same plane that do not intersect.
perpendicular lines
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 $mm$ and containing the point $(x1,y1)(x1,y1)$ is $y−y1=m(x−x1)y−y1=m(x−x1)$.
positive slope
A positive slope of a line goes up as you read from left to right.
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’.
rise
The rise of a line is its vertical change.
run
The run of a line is its horizontal change.
slope formula
The slope of the line between two points $(x1,y1)(x1,y1)$ and $(x2,y2)(x2,y2)$ is $m=y2−y1x2−x1m=y2−y1x2−x1$.
slope of a line
The slope of a line is $m=riserunm=riserun$. The rise measures the vertical change and the run measures the horizontal change.
slope-intercept form of an equation of a line
The slope–intercept form of an equation of a line with slope $mm$ and y-intercept, $(0,b)(0,b)$ is, $y=mx+by=mx+b$.
solution of a linear inequality
An ordered pair $(x,y)(x,y)$ is a solution to a linear inequality the inequality is true when we substitute the values of x and y.
vertical line
A vertical line is the graph of an equation of the form $x=ax=a$. The line passes through the x-axis at $(a,0)(a,0)$.
x- intercept
The point $(a,0)(a,0)$ where the line crosses the x- axis; the x- intercept occurs when $yy$ is zero.
x-coordinate
The first number in an ordered pair $(x,y)(x,y)$.
y-coordinate
The second number in an ordered pair $(x,y)(x,y)$.
y-intercept
The point $(0,b)(0,b)$ where the line crosses the y- axis; the y- intercept occurs when $xx$ is zero.
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