4: Graphing Lines
- Page ID
- 61382
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- 4.1: Rectangular Coordinate System
- The rectangular coordinate system consists of two real number lines that intersect at a right angle. The horizontal number line is called the x -axis, and the vertical number line is called the y-axis. These two number lines define a flat surface called a plane, and each point on this plane is associated with an ordered pair of real numbers (x,y). The first number is called the x-coordinate, and the second number is called the y-coordinate. The intersection is the origin: (0,0).
- 4.2: Graph by Plotting Points
- A linear equation with two variables has standard form ax+by=c , where a,b , and c are real numbers and a and b are not both 0. Solutions to equations of this form are ordered pairs (x,y) , where the coordinates, when substituted into the equation, produce a true statement.
- 4.4: 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.
- 4.5: 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.