4The Coordinate Plane Axes – two perpendicular number lines. Origin – where the axes intersect at their zero points.X-axes – The horizontal number line.Y-axis – The vertical number line.Coordinate plane – the plane containing the x and y axes.12345-1-2-3-4-5yx12345-1-2-3-4-5Origin (0,0)
5Quadrants12345-1-2-3-4-5yQuadrants – the x-axis and y-axis separate the coordinate plane into four regions.Notice which quadrants contain positive and negative x and y coordinates.III(–,+)(+,+)x12345-1-2-3-4-5IIIIV(–, –)(+, –)
6Coordinates (2, 3) (2, 3) (0, 0) origin move right 2 units 12345-1-2-3-4-5yTo plot an ordered pair, begin at the origin, the point (0, 0), which is the intersection of the x-axis and the y-axis.(2, 3)(0, 0)xThe first coordinate tells how many units to move left or right; the second coordinate tells how many units to move up or down.12345-1-2-3-4-5originmove right 2 units(2, 3)move up 3 unitsx-coordinate move right or lefty-coordinate move up or downTo graph an ordered pair means to draw a dot at the point on the coordinate plane that corresponds to the ordered pair.
8Vocabulary Transformation – movements of geometric figures Preimage – the position of the figure before the transformationImage – the position of the figure after the transformation.Reflection – a figure is flipped over a line (like holding a mirror on it’s edge against something)Translation – a figure is slid in any direction (like moving a checker on a checkerboard)Dilation – a figure is enlarged or reduced.Rotation – a figure is turned about a point.
17VocabularyEquation in two variables – an equation that has two variablesSolution – in the context of an equation with two variables, an ordered pair that results in a true statement when substituted into the equation.
18Different Ways to Solve Solving using a replacement set – a variation of guess and check. You start with an equation and several ordered pairs. You plug each ordered pair into the equation to determine which ones are solutions.Solving Using a Given Domain – Start with an equation and a set of numbers for one variable only. You then substitute each number in for the variable it replaces, and solve for the unknown variable. This gives you a set of ordered pairs that are solutions.
19Dependent VariablesWhen you solve an equation for one variable, the variable you solve for becomes a “Dependent Variable”. It depends on the values of the other variable.Dependent VariableIndependent VariableThe values of “y” depend on what the value of “x” is.
21Vocabulary Linear equation – the equation of a line Standard form – Ax + By = C where A, B, and C are integers whose greatest common factor is 1, A is greater than or equal to 0, and A and B are both not zero.X-intercept – The X coordinate of the point at which the line crosses the x-axis (Y is equal to 0)Y-intercept – the Y coordinate of the point at which the line crosses the y-axis (X is equal to 0)
22Methods of Graphing Make a table – Use the Intercepts – Solve the equation for y.Pick at least 3 values for x and solve the equation for the 3 values of y that make the equation true.Graph the resulting x and y (ordered pair) on a coordinate plane.Draw a line that includes all points.Use the Intercepts –Make X equal to zero.Solve for Y.Make Y equal to zero.Solve for X.Graph the two coordinate pairs: (0,Y) and (X,0)Draw a line that includes both points.
24VocabularyFunction – a relation in which each element of the domain is paired with exactly one element of the range (for each value of x there is a value for y, but each value of y cannot have more than one value of x)Vertical line test – if no vertical line can be drawn so that it intersects the graph in more than one place, the graph is a functionFunction notation – f(x) replaces y in the equation.