Topic 1: Solve Equations

Abscissa: the name of the horizontal numberline (sometimes called the x-axis, but only when the variable is x)

Axis (Axes): a numberline used for reference, typically when graphing. "Axes" is plural.

Cartesian Coordinate Plane: the graphing plane which uses a horizontal and a vertical axis (abscissa and ordinate)

Consistent: describes a situation that has a solution (or many solutions)

Dependent: describes a situation with more than one solution

Direct Variation: a situation where increasing one value proportionally increases another, such as the more pounds of strawberries you buy, the more the total cost will be.

Equation: two expressions joined by a "="

Forms of the Line: different arrangements of the equation, used to highlight different features of the line

Identity: an equation that is always true, such as 2 + 2 = 4, or (1)(x) = x + 0

Inconsistent: describes a situation that has no solution

Independent: describes a situation with exactly one solution

Infinitely Many: an unlimited amount

Intercept: where the graph crosses an axis

Open Sentence: a statement that might be true or might be false, depending on the situation, such as x + 2 = 5, or x < 10. Both are true if x is 3, but both are false if x is 20.

Ordered Pair: a pair of values written in order, typically like (7, -2)

Ordinate: the name of the vertical numberline (sometimes called the y- axis, but only when the variable is y)

Origin: the starting point. On a numberline, that's 0. On the Cartesian coordinate plane, that's (0, 0).

Quadrant: one of the four regions of the Cartesian coordinate plane between the axes

Slope: the rate of change of a line (how steep it is)

Solution: a value for the variable (or a set of values for all of the variables) that makes the open sentence true

Solve: to find all of the solutions. Just because you found one does not mean you have solved it. To solve requires proof that all solutions have been found, or proof that no solutions exist.

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