We are given the attached graph. From the graph, we will calculate the slope of the lines as shown below:
Blue Line
[tex]\begin{gathered} \text{We will select any two coordinates that lie across the straight line. We have:} \\ (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(6,0) \\ \text{We will calculate the slope using the formula:} \\ slope,m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-(-3)}{6-0} \\ m=\frac{0+3}{6-0}=\frac{3}{6} \\ m=\frac{1}{2} \\ \\ \therefore m_{blue}=\frac{1}{2} \end{gathered}[/tex]
The slope of the blue line is: 1/2
We test for perpendicularity using the slopes. For perpendicular lines, the product of their slopes is -1. We thus calculate the slope of the green line:
[tex]\begin{gathered} m_{blue}\times m_{green}=-1 \\ \frac{1}{2}\times m_{green}=-1 \\ \text{We will make }m_{green}\text{ the subject of the formula. We have:} \\ \text{Multiply both sides by ''2'', we have:} \\ m_{green}=2(-1) \\ m_{green}=-2 \\ \\ \therefore m_{green}=-2 \end{gathered}[/tex]
For a line perpendicular to the blue line, its slope will be: -2
A graph of a line perpendicular to the blue line is shown below:
