Formula Review

5.1 Algebraic Expressions

• Distributive Property: a(b+c)=ab+aca(b+c)=ab+ac

5.3 Linear Inequalities in One Variable with Applications

• For any numbers aa, bb, and ,, if a<ba<b, then a+c<b+ca+c<b+c and a−c<b−ca−c<b−c.
• For any numbers aa, bb, and cc, if a>ba>b, then a+c>b+ca+c>b+c and a−c>b−ca−c>b−c.
• For any numbers aa, bb, and cc,
  multiply or divide by a positive:
  if a<ba<b and c>0c>0, then ac<bcac<bc and ac<bcac<bc
  if a>ba>b and c>0c>0, then ac>bcac>bc and ac>bcac>bc
  multiply or divide by a negative:
  if a<ba<b and c<0c<0, then ac>bcac>bc and ac>bcac>bc
  if a>ba>b and c<0c<0, then ac<bcac<bc and ac<bcac<bc

5.8 Graphing Functions

• To calculate slope (m)(m), use the formula
  m=riserunm=riserun,
  where the rise measures the vertical change and the run measures the horizontal change.
• To find the slope of the line between two points (x1,y1)(x1,y1) and (x2,y2)(x2,y2), use the formula
  m=y2−y1x2−x1