AlgebraLab

Algebra I Recipe: Standard Form Of A Linear Equation

By G Redden

A. Standard Form
  1. Ax + By = C
  2. A, B, C are integers (positive or negative whole numbers)
  3. No fractions nor decimals in standard form.
  4. Traditionally the "Ax" term is positive.
B. How to Write the Equation into Standard Form When Given an Equation
  1. If there are fractions:
    • Multiply each term in the equation by the LCD.
    • Add or subtract to get “x” and “y” on the same side and the number term on the opposite side.
  2. If there are decimals:
    • Multiply each term in the equation by 10, 100, 1000, etc.
    • Add or subtract to get “x” and “y” on the same side and the number term on the opposite side.
  3. If there are no fractions nor decimals:
    • Add or subtract to get “x” and “y” on the same side and the number term on the opposite side.
1.
4x - y - 7 = 0
2.
y = -5x + 2
3.
y = -0.4x + 1.2
4.
3x + 9 = (7/2)y
5.
y = 9x + ½
6.
y = (-¾)x + (5/4)
C. How to Write the Equation into Standard Form When Given the Slope and a Point on the Line
  1. Write the equation into y = mx + b using y - k = m (x - h).
    See Sec 5.2 for assistance.
  2. Change the equation into standard form Ax + By = C.
    See Sec 5.5 part B for assistance.
7.
(8, 3) and m = 4
8.
(-1, 4) and m = -1
9.
(3,-2) and m = 5
10.
(0, 3) and m = 1
D. How to Write the Equation into Standard Form When Given Two Points on the Line
  1. Find the slope using the formula.
  2. Write the equation into y = mx + b using y - k = m (x - h).
  3. Change the equation into standard form Ax + By = C.
11.
(4, 4) and (-2, -1)
12.
(1, 4) and (5, 7)
13.
(-4, 1) and (2, -5)
14.
(0, 0) and (2, 0)