3.In the figure, the straight line L:2x-y-18 = 0 cuts the x-axis and the y-axis atA and B respectively.L: 2x - y - 18 = 0(a)(i) Find the slope of L.(ii) Find the coordinates of A and B.(3 marks)b)Find the equation of the perpendicular bisector of AB in general form.​

Answer:see explanationStep-by-step explanation:The equation of a line in slope- intercept form isy = mx + c ( m is the slope and c the y- intercept )Rearrange 2x - y - 18 = 0 into this formSubtract 2x - 18 from both sides - y = - 2x + 18 ( multiply through by - 1 )y = 2x - 18 ← in slope- intercept formwith slope m = 2 and y- intercept B(0, - 18)To find the x- intercept let y = 0 in the equation and solve for x2x - 18 = 0 ( add 18 to both sides )2x = 18 ( divide both sides by 2 )x = 9Hence x- intercept A(9, 0)(b)The perpendicular bisector passes through the midpoint of AB at right angles.Given a line with slope m then the slope of a line perpendicular to it is[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]The midpoint of AB is[0.5(9 + 0), 0.5(0 - 18) ] = (4.5, - 9)Thusy = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equationTo find c substitute (4.5, - 9) into the partial equation- 9 = - 2.25 + c ⇒ c = - 9 + 2.25 = - 6.75 = - [tex]\frac{27}{4}[/tex]y = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{27}{4}[/tex] ← in slope- intercept formMultiply through by 44y = - 2x - 27 ( subtract - 2x - 27 from both sides )2x + 4y + 27 = 0 ← in general form