Choose an equation for the line that is parallel to the given line and passes through the given point for questions 1 and 2. y=5x+10; (2,14) a. y= 1/5x+4 b. y= -1/5x-4 c. y=5x-68 d. y=5x+4 2. y=1/5x-10; (15,-16) a. y=-5x+19 b. y=1/5x+91/5 c. y=1/5x-19 d. y=5x-19 5. choose the equation of a line that is perpendicular to the given line and that passes through the given point 4x-12y=2; (10,-1) a. y=3x+29 b. y=-1/3x+29 c. y=-3x+29 d. y=-1/3x+7

To solve each of the problems, I first looked for the equation that had the same slope value and then plugged in the 'x' coordinate to see if it gave me the correct 'y' coordinate.

1.)
     D.) y = 5x + 4
          14 = 5(2) + 4
          14 = 10 + 4
          14 = 13

2.)
     C.) y = 1/5x - 19
        -16 = 1/5 (15) - 19
        -16 = (3) - 19
        -16 = -16

3.) First, get 'y' by itself by subtracting 4x from both sides and dividing the whole equation by -12. To find perpendicular lines, the slope must be the opposite reciprocal of the first slope (in this case, flip the fraction to get the three on top). Add the opposite sign to the slope as your final step.

4x - 12y = 2
-4x            -4x
-12y = -4x + 2
-12y / -12 = -4x / -12+ 2 / -12
y = 1/3x - 1/6

C.) y = -3x + 29
     -1 = -3(10) + 29
     -1 = (-30) + 29 
     - 1 = -1