### 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:

$$\begin{array}{cccccccccc}\hfill Ax+By>C\hfill & & & \hfill Ax+By\xe2\u2030\yen C\hfill & & & \hfill Ax+By<C\hfill & & & \hfill Ax+By\xe2\u2030\xa4C\hfill \end{array}$$

where $A\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}B$ 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.

- pointâ€“slope form
- The pointâ€“slope form of an equation of a line with slope $m$ and containing the point $\left({x}_{1},{y}_{1}\right)$ is $y\xe2\u02c6\u2019{y}_{1}=m\left(x\xe2\u02c6\u2019{x}_{1}\right)$.

- 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 â€˜coordinate planeâ€™.

- 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 $m=\frac{{y}_{2}\xe2\u02c6\u2019{y}_{1}}{{x}_{2}\xe2\u02c6\u2019{x}_{1}}$.

- 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 slopeâ€“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.