Question

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

Answer 1

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