Chapter 5.6, Problem 25PPE

To determine

To calculate: Equation representing the path

Answer to Problem 25PPE

The equation representing the path is $y=-\frac{1}{2}x+4$

Explanation of Solution

Given information: path is perpendicular to the main street, passing through $(0,4)$ ( path entrance)

Calculation:

From the graph, lets first try to find out the equation of a main street.

Now, from the graph we can see, line is passing through points $(x_1,y_1)=(2,1)$ and $(x_2,y_2)=(3,3)$

From these two points,

Equation of the main street line will be,

  $\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}$

  $\therefore \frac{x-2}{3-2}=\frac{y-1}{3-1}$

  $\therefore 2x-y=3$ or $y=2x-3$ , slope is $2$

Now, path is perpendicular to the main street, therefore slope of the equation of path will be $-1/2$

  $\therefore$ The equation of a line will be $y=-\frac{1}{2}x+c$

Now, the line is passing through point $(0,4)$ . By using this information,

The equation of a path line will be $y=-\frac{1}{2}x+4$