Chapter 14.2, Problem 35WE

To determine

To calculate the equation from the given points.

Answer to Problem 35WE

The equation is obtained as,

$y=-x+c$

Explanation of Solution

Given information:

The given points are $\left(5,1\right)\text{ and }\left(1,\text{ 5}\right)$

Concept used:

  $\begin{array}{l}y=mx+c\\ \text{where}\\ m=\frac{y_2-y_1}{x_2-x_1}\end{array}$

Calculation:

The line of the given points can be obtained as,

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{5-1}{1-5}\\ m=\frac{4}{-4}\\ m=-1\\ y=-1\cdot x+c\\ y=-x+c\left[\text{where c is constant}\right]\end{array}$

Therefore, the equation is obtained as,

  $y=-x+c$