Question

Write the slope-intercept form of the equation that is described below.

Through (3, 3) and perpendicular to y = 14x − 2

What is the equation?

Answer 1

y = -¹/₁₄x + 3³/₁₄

Explanation:

If two lines are perpendicular then the product of theirs slopes is equal -1:

y=m₁x+b₁ ⊥ y=m₂x+b₂ ⇒ m₁×m₂ = -1

y = 14x - 2 ⇒ m₁=14

14×m₂ = -1 ⇒ m₂ = -¹/₁₄

The line y=-¹/₁₄x+b passes through point (3, 3) so the equation:

3 = -¹/₁₄×3 + b must be true

3 = -³/₁₄ + b

b = 3³/₁₄

Therefore equation in slope-intercept form:

y = -¹/₁₄x + 3³/₁₄