Question

Write the equations of the line that passes through the point 4,3) and is perpendicular to the line y=2x−4 . Write the equation in slope-intercept form.

Answer 1

y = -¹/₂x + 5

Explanation:

The product of slopes of perpendicular lines is -1

y = 2x − 4 ⇒ m₁ = 2

m₁m₂ = -1

2m₂ = -1

m₂ = -¹/₂

The Point-Slope form of equation of a line with slope of "m" and passing through point (x₁, y₁) is: y - y₁ = m(x - x₁)

m = -¹/₂

(4, 3) ⇒ x₁ = 4, y₁ = 3

So the equation in point-slope form:

y - 3 = -¹/₂(x - 4)

Therefore:

y - 3 = -¹/₂x + 2

y = -¹/₂x + 2 + 3

y = -¹/₂x + 5