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Key Terms Chapter 04: Graphs

Last updated

Apr 2, 2025
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- Key Terms Chapter 03: Math Models
- Key Terms Chapter 05: Systems of Linear Equations

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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:
$Ax+By>C \qquad Ax+By≥C \qquad Ax+By<C \qquad Ax+By≤C$
where $A$ 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 $(x_1,y_1)$ is $y−y_1=m(x−x_1)$ .

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, /((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.

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