Question

A bridge being designed will crossthe river at a right angle. Theequation of the left bank of theriver is y = 2x + 8. The center ofthe bridge will pass through (0, 2).What is the equation of the linerepresenting the bridge?

Answer 1

Let's begin by listing out the information given to us:

Left side: y = 2x + 8

Center of the bridge: (0, 2)

`\begin{gathered} y=2x+8 \\ m=2 \\ \text{However, the bridge is perpendicular to }y=2x+8\colon \\ m(perpendicular)=-(1)/(m) \\ m(perpendicular)=-(1)/(2) \end{gathered}`

Use the point-slope formula to get the equation of the bridge:

`\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(0,2);m=m(perpendicular)=-(1)/(2) \\ y-2=-(1)/(2)(x-0) \\ y-2=-(1)/(2)x \\ y=-(1)/(2)x+2 \\ \\ \therefore\text{ equation of the line representing the bridge is }y=-(1)/(2)x+2 \end{gathered}`