Question

Find an equation of the line L.

Short answer

The equation of line is$x+2y=5$

Step-by-step solution

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.

role="math" localid="1645947319658" $$\begin{gathered} y-y_1=m(x-x_1) \\ y-2=-\frac{1}{2}(x-1) \\ y-2=-\frac{x}{2}+\frac{1}{2} \\ y=-\frac{x}{2}+\frac{5}{2} \\ 2y=-x+5 \\ x+2y=5 \end{gathered}$$