Chapter 6, Problem 1PFA

To determine

To find: The slope of line perpendicular to given line.

Answer to Problem 1PFA

The slope of the line perpendicular to the line $x+2y=-3$ is 2.

Explanation of Solution

Given information:

The given line is $x+2y=-3$ .

Formula used:

The slope form of a straight line is $y=mx+c$ .The product of slopes of two perpendicular lines is -1.

Calculations:

The slope form of the given line is $y=-\frac{1}{2}x-\frac{3}{2}$ , therefore the slope of line $x+2y=-3$ is $-\frac{1}{2}$ . Let the slope of line perpendicular to given line is $m$ , the by the property of two perpendicular lines

  $m\times \left(-\frac{1}{2}\right)=-1$

  $\Rightarrow m\times \left(-\frac{1}{2}\right)=-1\times \left(-\frac{2}{1}\right)=2$

Thus, the slope of the line perpendicular to the line $x+2y=-3$ is 2.

Conclusion:

The slope of the line perpendicular to the line $x+2y=-3$ is 2.