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.

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

it is a reproduction.

step-by-step explanation: