Question

find the equation of the line passing through the points (3,-7) and (-2,-5)

Answer 1

the equation of a line in slope-intercept form is. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ∣ ∣ ∣ 2 2 y = m x + b 2 2 ∣ ∣ ∣ −−−−−−−−−−−−−−− where m is the slope and b the y-intercept to calculate m use the gradient formula ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ∣ ∣ ∣ 2 2 m = y 2 − y 1 x 2 − x 1 2 2 ∣ ∣ ∣ −−−−−−−−−−−−−−−−− let ( x 1 , y 1 ) = ( 3 , − 7 ) and ( x 2 , y 2 ) = ( − 2 , 4 ) ⇒ m = 4 − ( − 7 ) − 2 − 3 = 11 − 5 = − 11 5 ⇒ y = − 11 5 x + b ← partial equation to find b substitute either of the 2 given points into the partial equation using ( − 2 , 4 ) 4 = 22 5 + b ⇒ b = − 2 5 ⇒ y = − 11 5 x − 2 5