(a).

The given line is .

above line is slope - intercept form .

So, given line has a slope of() = 3.

So, a line parallel to it has a slope of  .

Because you know the slope and a point on the line,

Use point - slope form to write an equation of the line.

Let =   and slope() = 3.

          (Substitute 2 for , 4 for and = 3)

Rewrite in slope - intercept form .

                    (Product of two sames signs is positive)

                 (Apply distributive property: )

                     (Multiply: )

According to subtraction property of equality: a = b then a c = b c.

         (Subtract 2 from each side)

              (Apply additive inverse property: )

                     (Apply additive identity property: )

                          (Subtract: )

The equation of the line is  .

(b).

The given line is .

above line is slope - intercept form .

So, given line has a slope of() = 3.

So, a line perpendicular to it has a slope of  .

Because you know the slope and a point on the line,

Use point - slope form to write an equation of the line.

Let =   and slope() = .

          (Substitute 2 for , 4 for and = )

Rewrite in slope - intercept form .

                    (Product of two sames signs is positive)

           (Apply distributive property: )

                  (Multiply: )

         (Subtract 2 from each side)

              (Apply additive inverse property: )

                     (Apply additive identity property: )

To add fractions the denominators must be equal.

Find the least common denominator (LCD).

Write the prime factorization of each denominator.

Multiply the highest power of each factor in either number.

LCD of the fractions is 3.

Rewrite the equivalent fractions using the LCD.

Rewrite the expression using the LCD.

     (Subtract: )

The equation of the line is  .