Question

write an equation in slope-intercept form for the line that passes through (-2,5) and is perpendicular to the line described by y=-2x+6

Answer 1

y = ¹/₂x + 6

Explanation:

The product of slopes of perpendicular lines is -1

y = - 2x + 6 ⇒ m₁ = - 2

m₁m₂ = -1

-2m₂ = -1

m₂ = ⁻¹/₋₂ = 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

(-2, 5) ⇒ x₁ = -2, y₁ = 5

So the equation in point-slope form:

y - 5 = ¹/₂(x - (-2))

Therefore:

y - 5 = ¹/₂x + 1

y = ¹/₂x + 1 + 5

y = ¹/₂x + 6