Find the equation of a line that is parallel to \(y=3x-5\) and passes through the point \((1,2)\).
\(y=3x-1\)
We need the line that is parallel to \(y=3x-5\) and passes through the point \((1,2)\).
The key fact is that two non-vertical lines are parallel exactly when their slopes are equal. So first read off the slope of the given line.
Comparing \(y=3x-5\) with the slope-intercept form \(y=mx+c\), the coefficient of \(x\) gives the slope \(m=3\).
The required line has the same slope, so it can be written as \(y=3x+c\), where only the intercept \(c\) remains to be found.
Force the line through \((1,2)\) by substituting \(x=1,\ y=2\): \(2=3(1)+c\).
Solve for the intercept: \(2=3+c\Rightarrow c=2-3=-1\).
Combining the shared slope with this intercept gives the line. The equation is \(y=3x-1\).
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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.
