Find an equation of the line perpendicular to the graph of 4x-2y=9 that passes through the point at ( 2, 6 )

y = -½x + 7

Step-by-step explanation:

A. Find the intercepts of the first graph

   4x - 2y = 9

(i)    Let x = 0

         -2y = 9     Divide each side by -2

            y = -9/2

(ii) Let y = 0

          4x = 9     Divide each side by 4

            x = 9/4

The line passes through the points (0, -9/2) and (9/4, 0).

B. Equation for perpendicular line

(i) Find the slope (m₁) of the original line

The equation for the original line is

4x - 2y = 9              Subtract 4x from each side

     -2y = -4x + 9     Divide each side by 2

        y = 2x - 9/2

slope = m₁ = 2

(ii) Find the slope (m₂) of the perpendicular line

m₂ = -1/m₁     Substitute the value of m₁

m₂ = -½

C. Find the equation for the perpendicular line

y =   mx + b     Substitute the value of m₂

y =  -½x + b

The line passes through (2, 6).  

6 = -½ × 2 + b

6 =      -1    + b     Add 1 to each side

b = 7  

y = -½x + 7

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

The blue line passing through (2, 6) is the perpendicular line.

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