Standard form solve equations

Standard form solve equations

• 1.
  Important Rules: StandardForm Ax + By = C Rules: • A is positive • A,B,C are whole #s • No fractions/decimals
• 2.
  Example 1 Convertthe equation to standard form: y = 2x + 4 -2x -2x -2x + y = 4 -1 -1 -1 2x – y = -4 *To make A positive, divide (or multiply) everything by -1
• 3.
  Example 2 Writean equation in standard form: m = 3/2 b = 12 y = 3x + 12 2 -3/2x -3/2x -3x + y = 12 2 -3x + 2y = 24 -1 -1 -1 3x – 2y = -24 (2) (2) (2) Plug into y = mx + b *To get rid of the fraction, multiply everything by the denominator.
• 4.
  Writing Equations ofa Line
• 5.
  Various Forms ofan Equation of a Line. Slope-Intercept Form Standard Form Point-Slope Form y mx b m b y      slope of the line intercept Ax  By  C A B C A A , , and are integers 0, must be postive    y  y  m x  x m  x y 1 1 slope of the line , is any point   1 1
• 6.
  EXAMPLE 1 Writean equation given the slope and y-intercept SOLUTION 3 4 From the graph, you can see that the slope is m = and the y-intercept is b = –2. Use slope-intercept form to write an equation of the line. y = mx + b Use slope-intercept form. 3 4 y = x + (–2) 3 4 Substitute for m and –2 for b. 3 4 y = x (–2) Simplify.
• 7.
  EXAMPLE 2 Writean equation given two points Write an equation of the line that passes through (5, –2) and (2, 10). SOLUTION The line passes through (x1, y1) = (5,–2) and (x2, y2) = (2, 10). Find its slope. y2 – y1 m = x2 – x1 10 – (–2) = 2 – 5 12 –3 = = –4
• 8.
  EXAMPLE 2 Writean equation given two points You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x1, y1) = (4, – 7). y2 – y1 = m(x – x1) Use point-slope form. y – 10 = – 4(x – 2) Substitute for m, x1, and y1. y – 10 = – 4x + 8 Distributive property y = – 4x + 8 Write in slope-intercept form.
• 9.
  Steps for Solving Two-Step Equations 1. Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation. 2. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.
• 10.
  Opposite Operations Addition Subtraction Multiplication  Division
• 11.
  Helpful Hints? Identifywhat operations are on the variable side. (Add, Sub, Mult, Div) “Undo” the operation by using opposite operations. Whatever you do to one side, you must do to the other side to keep equation balanced.
• 12.
  Ex. 1: Solve4x – 5 = 11 4x – 5 = 15 +5 +5 (Add 5 to both sides) 4x = 20 (Simplify) 4 4 (Divide both sides by 4) x = 5 (Simplify)