A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.
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Correct Answer: Option D
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: \(\frac{y-2}{x-(-1)} = \frac{y-2}{x+1} = \frac{-2}{3}\)
\(3y-6 = -2x-2 \implies 3y+2x = -2+6 =4\)
\(2x+3y = 6 \implies 3y = 6-2x\)
\(y = \frac{6}{3} - \frac{2x}{3}\)
Parallel lines have the same gradient
\(\therefore\) Gradient of the line = \(\frac{-2}{3}\)
Line passes through (-1,2)
Equation: \(\frac{y-2}{x-(-1)} = \frac{y-2}{x+1} = \frac{-2}{3}\)
\(3y-6 = -2x-2 \implies 3y+2x = -2+6 =4\)