Question

Find the equation of a line in slope intercept form, passing through (2,5) and parallel to 2x+3y=-12

Answer 1

`2x+3y=-12\ \ \ \Rightarrow\ \ \ 3y=-2x-12\ \ \ \Rightarrow\ \ \ y=- (2)/(3) x-4\\\\y=mx+b\ \ ||\ \ y=- (2)/(3) x-4\ \ \ \Leftrightarrow\ \ \ m=-(2)/(3)\\\\the\ point\ slope\ form:\ y-y_1=m(x-x_1)\ \ \ and\ \ \ (x_1,y_1)=(2,5)\\\\y-5=-(2)/(3)(x-2) \ \ \Rightarrow\ \ \ y-5=-(2)/(3)x+(4)/(3)\ \ \ \Rightarrow\ \ \ y=-(2)/(3)x+5+1(1)/(3) \\\\the\ slope\ intercept\ form:\ \ \ y=-(2)/(3)x+6(1)/(3)\\\\ the\ slope:\ m=- (2)/(3),\ \ \ the\ intercept:\ b=6(1)/(3)`