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The graph of which of the following equations is a straight line that is parallel to line l in the figure above?



Let's find the slope of line l first. l passes through the points (0,2) and (-3,0) and we know that

Slope of the line passing through the points \((x_1, y_1)\) and \((x_2, y_2)\) is given by, m = \(\frac{y_2 - y_1}{x_2 - x_1}\)
=> m = \(\frac{2 - 0 }{ ( 0 - (-3))}\) = \(\frac{2}{3}\)

We also know that if two lines are parallel then their slopes will be equal
=> Slope of the parallel line will also be \(\frac{2}{3}\)

Now, we need to find which of the lines given in the option choices has slope of \(\frac{2}{3}\)
We know that Slope of a general line ax + by + c = 0 is given by -(Coefficient of x) / (Coefficient of y) = \(\frac{-a}{b}\) = \(\frac{2}{3}\)

=> a can be -2 and b can b can be 3 or a can be 2 and b can be -3 or other choices.
=> line will be -2x + 3y = 0 or 2x - 3y = 0 or 3y - 2x = 0

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Co-ordinate Geometry