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 (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=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:

where AandB 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 (x1,y1) is y−y1=m(x−x1).

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 (x1,y1) and (x2,y2) is m=y2−y1x2−x1.

slope of a line
The slope of a line is m=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 m and y-intercept, (0,b) is, y=mx+b.

solution of a linear inequality
An ordered pair (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=a. The line passes through the x-axis at (a,0).

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