Chapter 1.3, Problem 59E

To determine

Equation of the line passing through $\left(2,\frac{1}{2}\right)$ and $\left(\frac{1}{2},\frac{5}{4}\right)$ , plot the line.

Answer to Problem 59E

The equation of the line passing through $\left(2,\frac{1}{2}\right)$ and $\left(\frac{1}{2},\frac{5}{4}\right)$ is $x+2y=3$

Explanation of Solution

Given info:

  $\begin{array}{l}(x_1,y_1)=\left(2,\frac{1}{2}\right)\\ (x_2,y_2)=\left(\frac{1}{2},\frac{5}{4}\right)\end{array}$

Formula used:

Equation of line passing through $(x_1,y_1)$ and $(x_2,y_2)$

  $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)(x-x_1)$

Calculation:

Equation of line is

  $\begin{array}{l}y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)(x-x_1)\\ y-\frac{1}{2}=\left(\frac{\frac{5}{4}-\frac{1}{2}}{\frac{1}{2}-2}\right)(x-2)\\ y-\frac{1}{2}=\left(\frac{\frac{6}{8}}{\frac{-3}{2}}\right)(x-2)\\ y-\frac{1}{2}=\left(\frac{-12}{24}\right)(x-2)\\ y-\frac{1}{2}=-\frac{1}{2}(x-2)\\ 2y-1=-x+2\\ x+2y=3\end{array}$

The equation of the line passing through $\left(2,\frac{1}{2}\right)$ and $\left(\frac{1}{2},\frac{5}{4}\right)$ is $x+2y=3$

Plot of the line is given by

  

Conclusion:

Thus,the equation of the line passing through $\left(2,\frac{1}{2}\right)$ and $\left(\frac{1}{2},\frac{5}{4}\right)$ is $x+2y=3$