Question

What is the equation in slope-intercept form of a line that is perpendicular to y=2x+2 and passes through the point (4, 3)?

Answer 1

Answer:   y = - ¹/₂ x + 5

Step-by-step explanation:

Find the slope of the perpendicular line

When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.

                 ⇒  if the slope of this line = 2     (y = 2x + 2)

                      then the slope of the perpendicular line (m) = - ¹/₂

Determine the equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:  

                               ⇒  y - 3 =  - ¹/₂  (x - 4)

We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

                             since   y - 3 =  - ¹/₂  (x - 4)

                                              y = - ¹/₂ x + 5   (in slope-intercept form)