Tell weather the lines through the given points are parallel perpendicular or neither

Answer:a)  Slope of line 1 = (2/3)b)  Slope of line 2 = (-3/2)c)  Two lines are perpendicular.Step-by-step explanation:Here, let the points of line 1 are A(1,0) and B(7,4)Let the points of line 2 are A(7,0) and B(3,6)Now for any two points,  the  slope m  of the line is given as : [tex]m = \frac{y_2 - y_1}{x_2-x_1}[/tex]⇒Slope of the line AB  = [tex]m1  =( \frac{4-0}{7-1})  = \frac{4}{6}    = \frac{2}{3}[/tex]or, m1  = 2/3and Slope of the line PQ  = [tex]m2  =( \frac{6-0}{3-7})  = -\frac{6}{4}    = -\frac{3}{2}[/tex]or, m2  = -3/2Now, TWO LINERS ARE SAID TO BE PERPENDICULAR if             m1 x  m2  = -1  :with heir respective slope m1 and m2 Here, [tex]m1 \times m2  = \frac{2}{3} \times \frac{-3}{2}   = -1[/tex]⇒ SLOPE OF AB x SLOPE OF PQ  =   -1Hence, Line AB is perpendicular to the line PQ.