Answer:
Perpendicular
Step-by-step explanation:
Lines that are parallel have the same slope, and lines that are perpendicular have an negative reciprocal slope.
To clarify, the reciprocal of 2 would be 1/2, and the negative reciprocal of 2 would be -1/2.
Calculate the slope of the lines by dividing the difference in y by the difference in x:
![m=\frac{y_2-y_1}{x_2-x_1}\\\\m_1=\frac{4-0}{7-1}=\frac{4}{6}=\frac{2}{3}\\\\m_2=\frac{6-0}{3-7}=\frac{6}{-4}=-\frac{3}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5Cm_1%3D%5Cfrac%7B4-0%7D%7B7-1%7D%3D%5Cfrac%7B4%7D%7B6%7D%3D%5Cfrac%7B2%7D%7B3%7D%5C%5C%5C%5Cm_2%3D%5Cfrac%7B6-0%7D%7B3-7%7D%3D%5Cfrac%7B6%7D%7B-4%7D%3D-%5Cfrac%7B3%7D%7B2%7D)
m₂ is the negative reciprocal of m₁, so these lines are perpendicular.
Showing the graph in the image as an example, though the equations only have the slope and not the y-intercept so the points wont be on the lines.