Question

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Answer 1

Answer:

perpendicular line:    y = -¹/₆ x + 4¹/₃

 parallel line:              y = 6x - 45

Step-by-step explanation:

y=m₁x+b₁   ⊥   y=m₂x+b₂   ⇔    m₁×m₂ = -1

{Two lines are perpendicular if the product of theirs slopes is equal -1}

y = 6x - 7   ⇒   m₁=6

6×m₂ = -1        ⇒    m₂ = -¹/₆

 

The line y=-¹/₆ x+b passes through point (8, 3) so the equation:

3 = -¹/₆ ×8 + b must be true

3 = -⁴/₃ + b

b = 4¹/₃

Therefore equation in  slope-intercept form:

                                                     y = -¹/₆ x + 4¹/₃

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

y = 6x - 7   ⇒   m₁=6   ⇒   m₂=6

The line y=6x+b passes through point (8, 3) so the equation:

3 = 6×8 + b must be true

3 = 48 + b

b = -45

Therefore equation in  slope-intercept form:

                                                     y = 6x - 45