Chapter 3, Problem 16CLR

To determine

To calculate: To find an equation of a line in standard from.

Answer to Problem 16CLR

The equation of the line in standard form is $x+2y=-2$ .

Explanation of Solution

Given information: The line passes through the point $\left(4,-3\right)$ and has slope $-\frac{1}{2}$ .

Formula used: The equation of line passing through the point $\left(x_1,y_1\right)$ and having slope m in standard form is,

  $y-y_1=m\left(x-x_1\right)$

• Here, m is the slope of the line.

Calculation: It is given that the line passes through the point $\left(4,-3\right)$ and has slope $-\frac{1}{2}$ . Comparing the point $\left(4,-3\right)$ with $\left(x_1,y_1\right)$ ,

  $\begin{array}{c}{x}_1=4\\ y_1=-3\end{array}$

Also,

  $m=-\frac{1}{2}$

Substitute these values in $y-y_1=m\left(x-x_1\right)$ ,

  $\begin{array}{c}y-y_1=m\left(x-x_1\right)\\ y-\left(-3\right)=-\frac{1}{2}\left(x-4\right)\\ y+3=-\frac{1}{2}\left(x-4\right)\\ 2y+6=-x+4\\ x+2y=4-6\\ x+2y=-2\end{array}$

Hence, the equation of the line in standard form is $x+2y=-2$ .