It is known that the direction vector of the line L1 is a = (1,3), and the direction vector of the line L2 is b = (- 1, K). If the line L2 passes through the point (0,5), the direction vector of the line L2 is b = (- 1, K), And L1 is perpendicular to L2?

It is known that the direction vector of the line L1 is a = (1,3), and the direction vector of the line L2 is b = (- 1, K). If the line L2 passes through the point (0,5), the direction vector of the line L2 is b = (- 1, K), And L1 is perpendicular to L2?

a·b=0
－1+3k=0,k=1/3
The slope is K / (- 1) = - 1 / 3
Point (0,5)
y-5=(-1/3)x

It is known that the line L with slope k passes through point P (4,2) and intersects the positive half axis of x-axis and y-axis with two points a and B
(1) Let the area of △ AOB be s, and let K denote s s;
(2) Find the minimum value of S and the equation of the line l when the minimum value is obtained

y=kx+b
2=4k+b
b=2-4k
y=kx+2-4k
Intersection with X, Y axis ((4k-2) / K, 0), (0,2-4k)
S=1/2︳4k-2︳︳2-4k︳=2(2k-1）^2

Through M (1,1), make a straight line L to intersect the positive half axis of X, Y axis and two points AB respectively. Let the slope of the straight line l be K and the area of the triangle OAB be s
Finding the functional relation between K and S S = f (k)
Find the minimum value of S and the corresponding linear l equation

If the slope of the straight line passing through the point m (1,1) is k, then the linear equation is y = K (x-1) + 1, so y = 0 is brought into the solution of the equation to get x = - 1 / K + 1, so a (- 1 / K + 1,0) brings x = 0 into the solution of the equation to get y = 1-k, so B (0,1-k) because the straight line intersects the positive half axis of X and Y axis, so - 1 / K + 1 > 0, 1-k > 0 two inequalities are solved to get K

If the slope of line L1 is 2, L1 ‖ L2, and line L2 passes through point (- 1,1) and intersects with y axis at point P, then the coordinate of point P is ()
A. （3，0）B. （-3，0）C. （0，-3）D. （0，3）

Because the slope of the line L1 is 2, L1 ‖ L2, the slope of the line L2 is also equal to 2, and the line L2 passes through the point (- 1, 1), so the equation of the line L2 is Y-1 = 2 × (x + 1), that is, y = 2X + 3, take x = 0, and the intersection point P of the line L2 and the Y axis is (0, 3)