find the slope of the line through (2,1) and (4,-5)

Answer 1

(2,1) and (4,-5) have a line through them with slope = the difference in y coordinates divided by the difference in corresponding x coordinates: slope = (1- -5)/(2-4) = (1+5)/-2 = 6/-2 = - 3

you could have done it in the reverse order: slope = (-5-1)/(4-2) = -6/2 = -3

the line's equation is slope = slope

using either point (2,1) or (4,-5) and a generic point (x,y)

(y-1)/x-2) = -3

simplify

y-1 = -3(x-2) = -3x +6

y = -3x +6+1

y =-3x + 7 where -3 is the slope and 7 is the y intercept