Linear Equations

Slope Intercept form

• y = mx + b

If you solve an equation for y, it is in slope intercept form!  The number that is in the place of b is the y intercept.  The number in the place of m (the coefficient of x) is the slope!

• positive slope - the line goes up and to the right (or down and left)
• negative slope - the line goes up and to the left (or up and right)

Using Intercepts

• To find x and y intercepts...do this  
• To find the x intercept, make y zero and solve the resulting equation for x
• when you get and answer...lets call it a.  Then the x intercept is (a, 0)
• To find the y intercept, make x zero and solve the resulting equation for y
• when you get and answer...lets call it b.  Then the y intercept is (0, b)

These two points (a,0) and (0,b) can then be used to graph the line!

Methods for finding slope

• Formula
• Solve an equation for y (put it in slope intercept form...y = mx + b)
• Ax + By = C is standard form....slope is -A/B!

Parallel and Perpendicular lines

• Parallel lines...same slope
• Perpendicular lines negative reciprocal slope

Finding the zeros

• Set the equation up equal to zero and solve...the resulting x value is called the zero.
• Usually the equations will be written using function notation
• y = 3x + 7 (linear notation...because of the y =)
• f(x) = 3x + 7 (function notation...because f(x) replaces y =)
• to find the zero...3x + 7 = 0, solve for x...x = -7/3
• -7/3 is called the zero, or root, solution and x intercept...it all means the same thing!  Like saying "hello" in different languages!

Domain and Range
  Relation is a set of ordered pairs

• Domain is the set of all x values of a relation
• Range is the set of all y values of a relation

• you can describe the domain by using inequalities x > -3
• y approaches +∞ (this is a neat use of using html code to get the symbol...read my post above)