Key Terms

boundary line

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

geoboard

A geoboard is a board with a grid of pegs on it.

graph of a linear equation

The graph of a linear equation $Ax+By=C$ 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 $y=b$. 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

A linear equation is of the form $Ax+By=C$, 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:

$$\begin{array}{cccccccccc}\hfill Ax+By>C\hfill & & & \hfill Ax+By\ge C\hfill & & & \hfill Ax+By<C\hfill & & & \hfill Ax+By\le C\hfill \end{array}$$

where $A\text{and}B$ 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 $(x,y)$ gives the coordinates of a point in a rectangular coordinate system.

origin

The point $(0,0)$ 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 $m$ and containing the point $\left(x_1,y_1\right)$ is $y-y_1=m\left(x-x_1\right)$.

positive slope

A positive slope of a line goes up as you read from left to right.

quadrant

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 $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

slope of a line

The slope of a line is $m=\frac{\text{rise}}{\text{run}}$. 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 $m$ and y-intercept, $\left(0,b\right)$ is, $y=mx+b$.

solution of a linear inequality

An ordered pair $\left(x,y\right)$ 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 $x=a$. The line passes through the x-axis at $\left(a,0\right)$.

x- intercept

The point $\left(a,0\right)$ where the line crosses the x- axis; the x- intercept occurs when $y$ is zero.

x-coordinate

The first number in an ordered pair $(x,y)$.

y-coordinate

The second number in an ordered pair $(x,y)$.

y-intercept

The point $\left(0,b\right)$ where the line crosses the y- axis; the y- intercept occurs when $x$ is zero.