Question

Find the equation of the line that passes through the points (-4, 2) and (5, -3). (*Hint: y=mx+b)

Answer 1

`y=-(5)/(9)x-(2)/(9)`

Explanation:

`(-4,2)=(x_1,y_1)\\(5,-3)=(x_2,y_2)\\`

Substitute values into the given equation ;

`(y-y_1)/(x-x_1)= (y_2-y_1)/(x_2-x_1) \\\\(y - 2)/(x - (-4))= (-3-2)/(5-(-4))\\ \\Simplify \\(y-2)/(x +4)= (-3-2)/(5+4) \\\\(y-2)/(x+4)= (-5)/(9) \\\\Cross\:Multiply\\9(y-2)=-5(x+4)\\\\Expand\\9y -18=-5x -20\\\\Collect\:like\:terms\\9y = -5x-20+18\\\\9y = -5x -2\\\\Divide \:through \:by \: 9\\\\(9y)/(9) = -(5)/(9) x -(2)/(9) \\\\y = -(5)/(9) x -(2)/(9) \\`