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 \(3x - 2y = 10\).
Similar Questions
What is the x-intercept of the line given by \(2x-3y=12\)?
Find the equation of a line that is parallel to \(y=3x-5\) and passes through the point \((1,2)\).
The coordinates of the vertices of a triangle are \(A(0,0),\ B(8,0),\) and \(C(0,6)\). What is the location of the orthocenter?
A drone flies along \(y = -x + 10\). Another follows \(y = x - 4\). At what point do they intersect?
A land plot is defined by points A(0,0), B(4,0), C(5,3), D(1,3). What is the area of the parallelogram representing this plot?
The equation of a line is \(2x-3y=6\). What is the slope of the line?
Find the equation of the line with slope -2 passing through the point (3, 5).
A triangle has vertices with coordinates A(1,2), B(5,2), and C(3,8). What is the y-coordinate of its centroid?
A line passes through the point (5, 7) and has a slope of -1. What is the equation of the line?
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)?
The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:
In which quadrant both abscissa and ordinate are negative?
Find the slope of the line joining the points (3, -4) and (5, 2).
Find the value of K for which equation x – Ky = 2, 3x + 2y = 5 has unique solution.
