Question

I need to know if the green line is perpendicular. I’m supposed to draw perpendicular line and then get the slope of those lines

Answer 1

We are given the attached graph. From the graph, we will calculate the slope of the lines as shown below:

Blue Line

`\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=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ m=(0-(-3))/(6-0) \\ m=(0+3)/(6-0)=(3)/(6) \\ m=(1)/(2) \\ \\ \therefore m_(blue)=(1)/(2) \end{gathered}`

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:

`\begin{gathered} m_(blue)* m_(green)=-1 \\ (1)/(2)* 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}`

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: