1: Graphs, Lines, and Inequalities
- Page ID
- 26483
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- 1.1: The Rectangular Coordinate Systems and Graphs
- Descartes introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Descartes named the horizontal axis the \(x\)-axis and the vertical axis the \(y\)-axis. This system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the \(x\)-axis and the \(y\)-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant.
- 1.2: Graph Using the y-Intercept and Slope
- In mathematics, we call the incline of a line the slope and use the letter m to denote it. The vertical change is called the rise and the horizontal change is called the run. The rise and the run can be positive or negative. A positive rise corresponds to a vertical change up and a negative rise corresponds to a vertical change down. A positive run denotes a horizontal change to the right and a negative run corresponds to a horizontal change to the left.
- 1.3: Finding Linear Equations
- Given the algebraic equation of a line, we are able to graph it in a number of ways. In this section, we will be given a geometric description of a line and be asked to find the algebraic equation. Finding the equation of a line can be accomplished in a number of ways, the first of which makes use of slope-intercept form, y=mx+b . If we know the slope, m , and the y -intercept, (0,b) , we can construct the equation.
- 1.4: Linear Inequalities and Absolute Value Inequalities
- In this section, we will explore various ways to express different sets of numbers, inequalities, and absolute value inequalities.
- 1.6: Polynomial and Rational Inequalities
- Solve polynomial and rational inequalities by using a sign chart.