Question

In each exercise $R_k:A\to A\text{'}$. Find an equation of line k.

Short answer

The equation is obtained as,

$y=-x+c$

Step-by-step solution

Step 1. Given Information.

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

Step 2. Concept Used.

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

Step 3. Calculation.

The line of the given points can be obtained as,

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

Step 4. Conclusion.

Therefore, the equation is obtained as,

$y=-x+c$