A line passes through the point (5, 7) and has a slope of -1. What is the equation of the line?
y = -x + 12
We need the equation of a straight line passing through the point \((5, 7)\) with slope \(m = -1\).
The most direct tool is the point-slope form of a line: \(y - y_{1} = m(x - x_{1})\).
Here \((x_{1}, y_{1}) = (5, 7)\) and \(m = -1\).
Substituting these values: \(y - 7 = -1(x - 5)\).
Expand the right side: \(y - 7 = -x + 5\).
Add 7 to both sides to isolate \(y\): \(y = -x + 5 + 7 = -x + 12\).
The key concept is the point-slope form, which builds a line's equation directly from one point and the slope.
Hence the equation of the line is y = -x + 12.
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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.
