Chapter 4.2, Problem 21PPS

To determine

To find: The equation of the straight line through the pair of points $\left(-2,-4\right)$ and $\left(2,4\right)$ .

Answer to Problem 21PPS

The equation of straight line is $y=5x+8$ .

Explanation of Solution

Given information:The given two pair of points through which the line passes are $\left(-2,-4\right)$ and $\left(2,4\right)$ .

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,

  $\begin{array}{c}y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ y-\left(-4\right)=\frac{4-\left(-4\right)}{2-\left(-2\right)}\left(x-\left(-2\right)\right)\\ y+4=\frac{8}{4}\left(x+2\right)\\ y+4=2\left(x+2\right)\mathrm{......}\left(1\right)\end{array}$

Further solving (1), the equation of the straight line is written as

  $\begin{array}{c}y+4=2\left(x+2\right)\\ y+4=2x+4\\ \text{or, }y=2x\end{array}$

Hence, the required equation of the straight line through the points $\left(-2,-4\right)$ and $\left(2,4\right)$ is $y=2x$ .