[tex]\begin{gathered} \text{for the line f we have 2 points:} \\ (x_1,y_1)=(2,4) \\ \text{and} \\ (x_2,y_2)=(3,-1) \\ \text{hence, the slope} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ is\text{ given by} \\ m=\frac{-1-4}{3-2} \\ m=-\frac{5}{1} \\ m=-5 \\ \text{now we ne}ed\text{ to find the slope for g} \end{gathered}[/tex][tex]\begin{gathered} \text{For g we have 2 points:} \\ (x_1,y_1)=(2,6) \\ (x_2,y_2)=(-3,7) \\ \text{hence, the slope is given by} \\ m=\frac{7-6}{-3-2} \\ m=\frac{1}{-5} \end{gathered}[/tex][tex]\begin{gathered} \text{parallel lines has the same slope.} \\ \text{perpendicular lines has reciprocal negative slope}\colon \\ m\Rightarrow-\frac{1}{m} \\ IN\text{ THIS CASE, they are neither parallel nor perpendicular since} \\ m=-5 \\ \text{and} \\ m=-\frac{1}{5} \\ \text{are not perpendicular } \end{gathered}[/tex]
