Download Pre-Algebra Notes Chapter 8

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.