The equation of three lines are given below Line 1: 2y= 5x +6 Line 2: y=2/5x-1 Line 3: 10x+4y=-6 For each pair of lines, determine whether they are parallel perpendicular or neither

Answer:The line 2 and Line 3 are perpendicular to each others But There is no relation between Line 1 and Line 2  , Line 1 and Line 3 Step-by-step explanation:Given as :The three line equation is Line 1 : 2 y = 5 x + 6Line 2 : y = [tex]\frac{2}{5}[/tex] x - 1Line 3 : 10 x + 4 y = - 6Now, The standard equation of line isy = m x + cwhere m is the slope of line And c is the y interceptSo, From Line 12 y = 5 x + 6or , y =  [tex]\frac{5}{2}[/tex] x + [tex]\frac{6}{2}[/tex] I.e y =  [tex]\frac{5}{2}[/tex] x + 3 So,  slope of this line = [tex]m_1[/tex] =  [tex]\frac{5}{2}[/tex] Again , From Line 2y = [tex]\frac{2}{5}[/tex] x - 1So, slope of this line =  [tex]m_2[/tex] =  [tex]\frac{2}{5}[/tex] Similarly , From Line 310 x + 4 y = - 6I.e 4 y = - 6 - 10 xor, y = - [tex]\frac{6}{4}[/tex] -  [tex]\frac{10}{4}[/tex] xI.e y =  - [tex]\frac{5}{2}[/tex] x  - [tex]\frac{6}{4}[/tex] So, Slope of this line = [tex]m_3[/tex] = - [tex]\frac{5}{2}[/tex] Now, If the lines are parallel , then the slope of the lines are equalAnd  If the lines are perpendicular , then the product of the slopes of the lines = - 1Now, From given lines[tex]m_2[/tex] × [tex]m_3[/tex] = [tex]\frac{2}{5}[/tex] × ( - [tex]\frac{5}{2}[/tex] )I.e [tex]m_2[/tex] × [tex]m_3[/tex] = - 1So, The line 2 and Line 3 are perpendicular to each others But There is no relation between Line 1 and Line 2  , Line 1 and Line 3Hence The line 2 and Line 3 are perpendicular to each others But There is no relation between Line 1 and Line 2  , Line 1 and Line 3 Answer