General Form

• The general form of a linear equation is Ax + By = C, where A, B and C are integers with no common factors and A is greater than zero. For example, 6x + 3y = 9 is not in general form because A, B and C share a factor of 3. Dividing all parts by three, you get the general form: 2x + y = 3.
  
  

Intercept-Intercept Form

• The intercept-intercept form, x/a + y/b = 1, occurs when the variables are set equal to a constant of 1. For example, 6x + 3y = 9 must be divided by 9 first to make this true. Then you get, 2/3(x) +y/3 = 1. To move the 2/3 (which was 6/9) into the denominator of x where it belongs, you have to reciprocate/flip the fraction. That is, x/(3/2) + y/3 = 1, where the x-intercept = 3/2 (3/2,0) and the y-intercept = 3 (0,3).
  
  

Slope-Intercept Form

• This form makes graphing easiest by displaying the y-intercept and the slope of the linear equation. It is a matter of arranging the equation into y = mx + b, where m = slope and b = y-intercept. For example, 6x + 3y = 9 becomes 3y = -6x + 9 and dividing by 3 gives you y = -2x + 3. Therefore, m = -2 and the y-intercept = (0, 3).
  
  

'Inverted' Slope-Intercept Form

• This form arranges for x = wy + a, where the inverse of "w" is m and "a" is the x-intercept. For example, 6x + 3y = 9 becomes 6x = -3y + 9 and dividing by 6 gives you x = (-1/2) y + 3/2, where the inverse of -1/2, which is -2, is the slope and the x-intercept = (3/2, 0).
  
  

Point-Slope Form

• Point-slope form is tailored to provide the general form or slope-intercept form of an equation by using a known slope and a point through that slope. For example, if we know m = 4 and the line passes through (2, 3), then the point-slop form is (y -- y1)/(x -- x1) = m or (y -- 3)/(x -- 2) = 4. From there, we could multiply by (x -- 2) and get y-3 = 4(x-2) = 4x -- 8. Add 3 to both sides and you have y = 4x -- 5, the slope-intercept form.