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Algebra Connections Glossary
y-axis   
  See “axes.”
y-coordinate   
  See “coordinate.”
y-intercept(s)   
  The point(s) where a graph intersects the y-axis.  A function has at most one y-intercept; a relation may have several.  The y-intercept of a graph is important because it often represents the starting value of a quantity in a real-world situation.  For example, on the graph of a tile pattern the y-intercept represents the number of tiles in Figure 0.  We sometimes report the y-intercept of a graph with a coordinate pair, but since the x-coordinate is always zero, we often just give the y-coordinate of the y-intercept.  For example, we might say that the y-intercept of the graph at right is (0, 2), or we might just say that the y-intercept is 2.  When a linear equation is written in y = mx + b form, b tells us the y-intercept of the graph.  For example, the equation of the graph below is y = x + 2 and its y-intercept is 2.

y = mx + b   
 

When two quantities x and y have a linear relationship, that relationship can be represented with an equation in y = mx + b form.  The constant m is the slope, and b is the y-intercept of the graph.  For example, the graph below shows the line represented by the equation y = 2x + 3, which has a slope of 2 and a y-intercept of 3.  This form of a linear equation is also called the slope-intercept form.

zero   
  A number often used to represent “having none of a quantity.”  Zero is neither negative nor positive.  Zero is the identity element for addition.
Zero Product Property   
  The Zero Product Property states that when the product of two or more factors is zero, one of these factors must equal zero.  That is, if a · b = 0, then either a = 0 or b = 0 (or both).  For example, if
(x + 4)(2x − 3) = 0, then either x + 4 = 0 or 2x − 3 = 0 (or both).  The Zero Product Property can be used to solve factorable quadratic equations.