Question

What is the equation of a line perpendicular to why=2x-6 that passes through (5,4)

Answer 1

Answer:

y = ½(13- x)

Step-by-step explanation:

Step 1. Find the slope (m₁) of the original line

The equation for the original line is

      y = 2x - 6

slope = m₁ = 2

Step 2. Find the slope (m₂) of the perpendicular line

m₂ = -1/m₁     Substitute the value of m₁

m₂ = -1/2

Step 3. Find the equation for the perpendicular line

y = mx + b     Substitute the value of m₂

y = -½x + b

The line passes through (5, 4).  

4 = -½(5) + b     Add 5/2 to each side

4 = -5/2 + b     Add 2 to each side

b = 13/2  

y = -½x + 13/2

y = ½(13 – x)  

In the image, below, the red line is the graph of your original equation.

The blue line passing through (5, 4) is the perpendicular line.