The coordinates of P and Q are (2,6) and (4,5) respectively. Equation of a line RS is Y= 2X -3. Determine if the lines are parallel or perpendicular

Answer:PerpendicularStep-by-step explanation:Given points P=(2,6) and Q=(4,5)The line RS is y=2x-3.Now we know that the line joining any two points (x1,y1) and (x2,y2) has slope m=[tex]\frac{y2-y1}{x2-x1}[/tex]Now the slope of the line PQ is m1=[tex]\frac{5-6}{4-2}[/tex]= -[tex]\frac{1}{2}[/tex] We know that  the slope of the line in the form y=mx+c is mSo the line RS has slope m2=2Now two lines are parallel if m1=m2And those two lines are perpendicular if [tex]m1*m2=-1[/tex]here m1= -[tex]\frac{1}{2}[/tex]    and m2=2clearly [tex]m1*m2=-1[/tex]Therefore the two given lines are perpendicular