Which of the following equations represents a line parallel to \(3x - 2y = 6\)?
\(3x - 2y = 10\)
Two straight lines are parallel exactly when they have equal slopes.
Writing a line as \(ax + by = c\), its slope is \(-\dfrac{a}{b}\) (rearranging to \(y = -\tfrac{a}{b}x + \tfrac{c}{b}\)).
For the given line \(3x - 2y = 6\): \(a = 3,\ b = -2\), so slope \(= -\dfrac{3}{-2} = \dfrac{3}{2}\).
A parallel line keeps the same \(x\) and \(y\) coefficients; only the constant on the right may differ.
The option \(3x - 2y = 10\) has slope \(-\dfrac{3}{-2} = \dfrac{3}{2}\), identical to the given line, so the two are parallel (and not the same line, since the constant differs).
Key idea: same coefficient ratio \(a:b\) means same slope. The required equation is \(3x - 2y = 10\).
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Important Questions from Co-ordinate Geometry
In which ratio the point (-3, p) divides the line segment joining the points (-5, -4) and (-2, 3)?
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
A1 (x1, y1), A2 (x2, y2), A3 (x3, y3) and A4 (x4, y4) are 4 points, p1 divides A1A2 in the ratio 1 ∶ 1, p2 divides P1A3 in the ratio 1 ∶ 2, P3 divides p2A4 in the ratio 1 ∶ 3. Then the coordinates of p3 are:
If (3, 2) are coordinates of the centroid of a triangle, whose vertices are (0, 4), (-2, 0) and (p, 2), then find the value of p.
