Chapter 1.4, Problem 23E

To determine

To find: standard form of equation for line $l$ .

Answer to Problem 23E

  $x+2y=-10$

Explanation of Solution

Given information:

The points on line are as follows:

  $A\left(x_1,y_1\right)=\left(-2,-4\right)$

  $\text{Slope},m=-\frac{1}{2}$

Calculation

The point slope form is as follows:

  $y-y_1=m\left(x-x_1\right)$ … (1)

Substitute the value of m and point of coordinates in equation (1) to get,

  $\begin{array}{c}y-\left(-4\right)=\left(-\frac{1}{2}\right)\left(x-\left(-2\right)\right)\\ y+4=-\frac{1}{2}\left(x+2\right)\\ y+4=-\frac{1}{2}x-1\\ y=-\frac{1}{2}x-1-4\\ y=-\frac{1}{2}x-5\\ 2y=-x-10\left[\text{By cross multiplying}\right]\\ x+2y=-10\end{array}$

Therefore, the standard equation of the line is $x+2y=-10$ .