Chapter 4.2, Problem 35PPS

To determine

To find: The equation of the straight line through the pair of points $\left(5,-3\right)$ and $\left(2,5\right)$ .

Answer to Problem 35PPS

The equation of straight line is $8x+3y-31=0$ .

Explanation of Solution

Given information: The given two pair of points through which the line passes are $\left(5,-3\right)$ and $\left(2,5\right)$ .

Formula used: Using two point form of the line, the equation of the line is written as

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

Calculation: Using the two point form of the line, the equation of the line is written as,

  $\begin{array}{c}y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\mathrm{......}\left(\begin{array}{l}\left(x_1,y_1\right)\to \left(5,-3\right)\\ \left(x_2,y_2\right)\to \left(2,5\right)\end{array}\right)\\ y-\left(-3\right)=\frac{5-\left(-3\right)}{2-5}\left(x-5\right)\\ y+3=-\frac{8}{3}\left(x-5\right)\\ 3\left(y+3\right)=-8\left(x-5\right)\mathrm{......}\left(\text{Cross}-\text{multiplying}\right)\end{array}$

Further solving, the equation of the straight line is written as

  $\begin{array}{c}3y+9=-8x+40\\ \text{or, }8x+3y-31=0\end{array}$

Hence, the required equation of the straight line through the points $\left(5,-3\right)$ and $\left(2,5\right)$ is $8x+3y-31=0$ .