1) Two known points on the line.Originally Posted byx-disturbed-x

First use the point-slope form (y-y1) = m(x-x1), then transform to the general form Ax +By +C = 0

m = (y2 -y1)/(x2 -x1)

m = (10 -4)/(2 -6) = 6/(-4) = -3/2

y -4 = (-3/2)(x -6)

Clear the fraction, multiply both sides by 2,

2y -8 = -3x +18

3x +2y -8 -18 = 0

3x +2y -26 = 0 ----------answer.

2) If point (-2,k) is on line L, then,

3(-2) +2(k) -26 = 0

-6 +2k -26 = 0

2k = 6 +26 = 32

k = 32/2 = 16 --------answer.

3.)

Line M is y -x +12 = 0

Line L is 3x +2y -26 = 0

If they intersect at point P, then their coordinates are the same at point P.

Or, the y of line M equals the y of line L at point P.

y -x +12 = 0

y = x -12 -------y of line M anywhere.

Substitute that into the equation of line L,

3x +2(x -12) -26 = 0

3x +2x -24 -26 = 0

5x -50 = 0

5x = 50

x = 50/5 = 10 -----the x-coordinate of point P.

Substitute that into the y of line M,

y = 10 -12

y = -2 ----the y-coordinate of point P

Therefore, point P is (10,-2) --------answer.

Check that on line M,

y -x +12 = 0

-2 -10 +12 =? 0

0 =? 0

Yes, so, OK.

On line L,

3x +2y -26 = 0

3(10) +2(-2) -26 =? 0

30 -4 -26 =? 0

0 =? 0

Yes, so, OK also.