A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.

Explanation

\(2x+3y = 6 \implies 3y = 6-2x\)

\(y = \frac{6}{3} - \frac{2x}{3}\) 

Parallel lines have the same gradient

\(\therefore\) Gradient of the line = \(\frac{-2}{3}\)

Line passes through (-1,2)

Equation: \(\frac{y-2}{x-(-1)} = \frac{y-2}{x+1} = \frac{-2}{3}\)

\(3y-6 = -2x-2 \implies 3y+2x = -2+6 =4\)