Problem 1: Use the FOIL method (2x + 1)(3x  1) = 6x^2  2x + 3x  1 = 6x^2 + x  1
Problem 2: Use the formula y = mx + b. m is your slope. y = 2x + b. Now plug in your coordinates into the x and y and solve for b.
5 = 2(3) + b
5 = 6 + b
1 = b so the equaton of the line is y = 2x + 1
Problem 3: If the slope of the lines is equal the lines are parallel. If the slopes are inverse and have opposite signs of each other the lines are perpendicular. If the slopes are not either of these then they are neither. First take the second equation and simplify it.
4x  2y = 6 Move the 4x over to other side using subtraction
2y = 6  4x Divide both sides by 2
y = 2x  6 2 is your slope which is equal to the slope of the first equation meaning your lines are parallel
Problem 4: 1/2(x  1) = 4 multiply both sides by 2
(x  1) = 8 move the 1 to the other side using addition
x = 9
Problem 5: (5x  2)^2 Use the FOIL method
(5x  2)(5x  2) = 25x^2  10x  10x + 4 Now simplify by combining like terms
25x^2  20x + 4
1/16/2013

Jeremy E.