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Algebra 2 Chapter 3
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Gravity
Terms in this set (48)
open sentences in two variables
An equation or inequality that contains two variables
solution (of an open sentence in the two variables x & y)
a pair of numbers, one a value of x and the other a value of y, that together make the sentence a true statement
ordered pair
How we usually write a solution, in which the value of x is listed first and the value of y is listed second
solution set (of an open sentence with 2 variables)
The set of all ordered pairs satisfying the sentence
solving (the open sentence)
Finding the solution set
plane rectangular coordinate system
A system for locating the point associated with any ordered pair by reference to two number lines intersecting at right angles
axes
Two number lines, one horizontal and one vertical, intersecting at point 0
origin
In a plane rectangular coordinate system, the meeting point of the axes; the graph of (0,0).
x-axis, y-axis
A horizontal and a vertical number line meeting at right angles, used in graphing points in the plane
quadrants
One of the four regions in which a plane rectangular coordinate system is divided by it's axes
graph (of an ordered pair)
The point in an xy- coordinate plane associated with an ordered pair of real numbers
coordinates of a point
The real number paired with that point on a number line
x-coordinate
The first coordinate in an ordered pair of real numbers associated with a point in the coordinate plane, also called the abscissa
y-coordinate
The second coordinate in an ordered pair of real numbers associated with a point in the coordinate plane; also called the ordinate
Cartesian coordinate system
Another name for the rectangular coordinate system, named after Rene Descartes, the French mathematician who introduced coordinates
graph (of an open sentence in two variables)
the set of all points in the coordinate plane whose coordinates satisfy the open sentence
linear equation in two variables
any equation that can be expressed in the form Ax + By = C (A and B not both 0, A > 0)
slope
For any two distinct points (x1, y1) and (x2, y2) on line L, the slope of L = (y2-y1) / (x2-x1)
What type of slope do vertical lines have?
Slope is undefined
What type of slope do horizontal lines have?
Slope is 0
What is the slope of the line Ax + By = C?
- A/B
Point Slope Form
y-y1 = m(x-x1)
standard form
Ax + By = C (A, B and C are integers)
slope-intercept form
y = mx + b (b is the y-int and m is the slope)
y-intercept
The y-coordinate of the point where a line or curve intersects the x axis
x-intercept
The x-coordinate of the point where a line or curve intersects the x-axis
system of linear equations, or a linear system
A set of linear equations in the same two variables
solution (of the system) or a simultaneous solution (of the equations)
Any ordered pair of numbers that is a solution of each equation in the system
Equivalent systems
systems that have the same solution set
linear combination
The result of adding two linear equations
consistent (equations)
If a system of equations has at least one solution
inconsistent (equations)
If a system of equations has no solution. Graphs are parallel lines.
dependent (equations)
If a consistent system has infinitely many solutions. Graphs are the same line.
linear inequality in two variables
When you replace the equals sign in a linear equation in two variables by one of the symbols <, >, </ or />
solution (of an inequality in two variables)
An ordered pair of numbers that satisfies the inequality
associated equation (of an inequality)
The equation from which an inequality is derived by replacing the equals sign by an inequality symbol
half-plane
The set of all points on one side of a given line, the boundary
graph of a system of inequalities
consists of points satisfying all of the inequalities in the system
mapping diagram
A diagram that pictures a correspondence between two sets
relation
Any set of ordered pairs
Function
A correspondence between two sets, D & R, that assigns to each member of D exactly one member of R
Domain
All x values for which the function is defined
What are 2 cases in which expressions are undefined in the real number system
1. division by zero
2. negatives under square roots
Range
All outputs that result from using the elements of the domain
graph of a function
the set of all points (x,y) such that x is in the domain of f and the rule of the function assigns y to x
values (of a function)
The members of its range
linear function
A function that can be defined by f(x) = mx + b (x, m & b real numbers)
constant function
if f(x) = mx + b and m = 0, then f(x) = b for all x, and its graph is the horizontal line y = b
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