Find the equation of the line with slope -2 passing through the point (3, 5).
\(y = -2x + 11\)
Given: slope \(m=-2\) and a point \((x_1,y_1)=(3,5)\) on the line.
Concept: the point-slope form of a straight line is \(y-y_1=m(x-x_1)\).
Substitute the values: \(y-5=-2(x-3)\).
Expand the right side: \(y-5=-2x+6\).
Add 5 to both sides: \(y=-2x+6+5\).
\(y=-2x+11\).
Hence the equation of the line is \(y=-2x+11\).
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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)?
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.
