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)?
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.
