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Pre-Algebra Notes Chapter 8 A relation is a set of ordered pairs that have something in common. The x-coordinates (also called the input values) form a set called the domain. The y-coordinates (also called the output values) form a set called the range. A relation is a function if for each input there is exactly one output. The vertical line test says that if you can find a vertical line passing through more than one point of the graph, then the relation is NOT a function. The solution of an equation in two variables is an ordered pair (x,y) that produces a true statement. The graph of an equation in two variables is the set of points in a coordinate plane that represent all the solutions. An equation whose graph is a line is called a linear equation. An equation that is solved for y is in function form. The x-coordinate where a graph crosses the x-axis is an x-intercept The y-coordinate where a graph crosses the y-axis is a y-intercept. The slope of a line is the ratio of the rise to the run between any two points on the line. A line that rises from left to right has a positive slope; a line that falls from left to right has a negative slope. A horizontal line has a slope of 0; a vertical line has an undefined slope. Use the formula: (y2 – y1)/(x2 – x1) to find the slope of a line passing through two given points (x1,y1) and (x2,y2). A linear equation of the form y = mx+ b is in slope-intercept form. The slope is m and the y-intercept is b. Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals of each other. (ex. : ½, -2) Function notation is when you replace the y with f(x) or g(x). A system of linear equations or simply a linear system, consists of two or more linear equations with the same variables. Example: y = 2x – 4 y = -3x + 1 A solution of a linear system in two variables is an ordered pair. This is the point where the two lines intersect. A linear inequality in two variables has >,<, ≤, or ≥ instead of an equal sign. A solution is an ordered pair that makes the statement true. The graph of a linear inequality represents all the solutions. Steps for graphing a linear inequality: 1. Graph the equation of the boundary line, determine whether it should be solid or dashed. 2. Test a point on one side of the line. 3. Shade the side that makes the statement true.