Q. 43 - Precalculus Enhanced with Graphing Utilities

Question

Find an equation of the line L.  

Step-by-Step Solution

Answer

The equation of line is $x+2y=5$

Step 1. Given Information

The given graph is 

Step 2. Explanation

From the given figure, we know the line is perpendicular to line $y=2x$

On comparing with the equation of line, we get the slope of line as 2 and as lines are perpendicular so the slope of the other line will be negative reciprocal of 2 which is $-\frac{1}{2}$

Substitute the values in the general form of equation of slope- line format.

$$\begin{gathered} y-y_1=m(x-x_1) \\ y-2=-\frac{1}{2}(x-1) \\ y-2=-\frac{x}{2}+\frac{1}{2} \\ y=-\frac{x}{2}+\frac{5}{2} \\ 2y=-x+5 \\ x+2y=5 \end{gathered}$$