Key Terms Chapter 04: Graphs
- Page ID
- 101921
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 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.