A line passes through `(x_(1), y_(1)) " and " (h, k)` . If slope of the line is m, show that ` k - y_(1) = m (h - x_(1))`.

Three points P (h, k), Q(x_(1) , y_(1))" and " R (x_(2) , Y_(2)) lie on a line. Show that (h - x_(1)) (y_(2) - y_(1)) = (k - y_(1)) (x_(2) - x_(1)) .

Prove that the line through the point (x_(1) , y_(1)) and parallel to the line Ax + By + C =0 " is " A (x - x_(1)) + B (y - y_(1)) = 0 .

If three points (h, 0),(a, b) and (0, k) lie on a line, show that a/h + b/k = 1 .

Find the slope of the lines : Passing through the points (3, -2) " and " (-1, 4)

A straight line passes through (h, k) and the middle point of the also (h, k). Show that the equation of straight line kx + hy = 2hk.

The points P divides the line - segment joining the points A(x_(1),y_(1))andB(x_(2),y_(2)) in the ratio m : n . If P lies on the line ax+by +c=0 , prove that, (m)/(n)=-(ax_(1)+by_(1)+c)/(ax_(2)+by_(2)+c) .

If a straight line passing through the focus of the parabola y^(2) = 4ax intersectts the parabola at the points (x_(1), y_(1)) and (x_(2), y_(2)) , then prove that x_(1)x_(2)=a^(2) .

If the image of the co-ordinate of a point (x_1,y_1) is (x_2,y_2) with respect to the straight line lx+my+n=0,then show that (x_2-x_1)/l=(y_2-y_1)/m=(-2(lx_1+my_1+n))/(l^2+m^2)

Find the equation of the line passing through (1,1) and parallel to the line 2x-3y+5=0.

Passing through the point (– 4, 3) with slope 1/2 then the equation of the line is?