Ais (-2,1) b is (6,5)c is (4,k) are all vertices of a right angled triangle abc. angle abc is the right angle. find an equation of a line that passes through a and c. give your answer in the form ay+bx=c where a, b and c are integersplz

1) in order to solve this problem you must to obtain The value of K,  for it you know by definition  that the  horizontal slope  of the side BC  is zero ,

then m = Y2-Y/X2-X1,   0 = 5-K/4-6⇒0 = 5-K⇒K = 5

known this value for K   you ca find the equation of thE line that pass through  A and C

2) Following the same procedure in first place you calculate the slope with the points A(-2,1) Y C ( 4,5)

m= 5-1/4-(-2) = 2

now with any point  A  or C and the slope you obtain the line

A(-2,1)

y-y1 = m (x-x1) ,   Y-1= 2(X-(-2)⇒Y-1= 2X+4⇒Y=2X+4-1⇒Y =2X+3

it has the same slope and a different y-intercept

hope this : )

step-by-step explanation: