help me solve (2x + 1) ( 3x - 1) / and find the equation of the line that goes through the point (3, -5) with slope -2

Question

Hello I need help can you please help me solve by showing me how you solve and not just the answer

Problem 1. perform the operation (2X = 1) (3X-1) I keep coming up with 5X, then i got 6X to the 2nd power - 1

Problem 2. Find the equation of the line that goes through the point (3, -5) w/ slope -2

Problem 3. Are the graphs of the following lines perpendicular, parallel or neither?

• y= 2X - 5
• 4X- 2y = 6

Problem 4. solve the following for X: 1/2( X- 1) = 4

Problem 5. Perform the operation (5X - 2) 2nd power

Answer 1

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