#"the distance d between a line "Ax +By+C=0#
#"and a point "(m,n)" is given by the formula"#
#color(red)(bar(ul(|color(white)color(black)(d=(|Am+Bn+C|)/(sqrt(A^2+B^2)))color(white)(2/2)|)))#
#"the equation of a line in "color(blue)"slope-intercept form"# is.
#•color(white)(x)y=mx+b#
#"where m is the slope and b the y-intercept"#
#"to calculate m use the "color(blue)"gradient formula"#
#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#
#"let "(x_1,y_1)=-4,2)" and "(x_2,y_2)=(3,-5)#
#rArrm=(-5-2)/(3-(-4))=(-7)/7=-1#
#rArry=-x+blarrcolor(blue)"partial equation"#
#"to find b substitute either of the 2 given points"#
#"into the partial equation"#
#"using "(3,-5)" then"#
#-5=-3+brArrb=-5+3=-2#
#rArry=-x-2color(blue)" is the equation of the line"#
#"we require the equation in the form "Ax+By+C=0#
#rArrx+y+2=0larrcolor(blue)"in general form"#
#"here "A=1,B=1" and "C=2,(m,n)=(1,2)#
#rArrd=(|1+2+2|)/(sqrt(1+1)#
#color(white)(rArrd)=5/sqrt2xxsqrt2/sqrt2=(5sqrt2)/2~~3.536#
