Question

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

Short answer

The equation is obtained as,

$y=\frac{3}{5}·x+c$

Step-by-step solution

Step 1. Given Information.

The given points are $\left(-1,2\right)\text{and}\left(4,5\right)$.

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,

$\begin{array}{c}m=\frac{y_2-y_1}{x_1-x_2}\\ m=\frac{5-2}{4-\left(-1\right)}\\ m=\frac{3}{5}\\ y=\frac{3}{5}\cdot x+c\left[\text{wherekisconstant}\right]\end{array}$

Step 4. Conclusion.

Therefore, the equation is obtained as,

$y=\frac{3}{5}\cdot x+c$