Answer:
The lines are not perpendicular
Explanation:
We are to calculate the slope from the information given to us and to determine if the lines are perpendicular. This is shown below:
Orange line
[tex]\begin{gathered} slope,m=\frac{rise}{run}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ slope,m=\frac{y_2-y_1}{x_2-x_1} \\ \text{From the ordered pair that lie along the orange line, we have:} \\ (x_1,y_1)=(0,0) \\ (x_2,y_2)=(3,2) \\ \text{Substitute these into the formula, we have:} \\ slope,m=\frac{2-0}{3-0} \\ slope,m=\frac{2}{3} \end{gathered}[/tex]Blue line
[tex]\begin{gathered} slope,m=\frac{rise}{run}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ slope,m=\frac{y_2-y_1}{x_2-x_1} \\ \text{From the ordered pair that lie along the blue line, we have:} \\ (x_1,y_1)=(0,0) \\ (x_2,y_2)=(-1,2) \\ \text{Substitute these into the formula, we have:} \\ slope,m=\frac{2-0}{-1-0} \\ slope,m=\frac{2}{-1}=-\frac{2}{1} \\ slope,m=-\frac{2}{1} \end{gathered}[/tex]For perpendicular lines, the relationship between their slope is that they are negative reciprocals of each other. This is given by the formula:
[tex]\begin{gathered} m=-\frac{1}{m_{perpendicular}} \\ \text{If the orange and blue lines are perpendicular, then this should be true:} \\ m_{orange}=-\frac{1}{m_{blue}} \\ \frac{2}{3}=\frac{-1}{-2} \\ \frac{2}{3}=\frac{1}{2}(FALSE) \\ \frac{2}{3}\ne\frac{1}{2} \\ \\ \therefore\frac{2}{3}\ne\frac{1}{2} \end{gathered}[/tex]Therefore, the lines are not perpendicular