Question 214449
1.) We want to find the slope of a line intersecting points (-2, 3) and (5,-8)  use the definition of slope.  SLOPE = (Y2 - Y1)/(X2 -X1) for points (X1, Y1) AND (X2, Y2).  (note the significance of parentheses )

Here, SLOPE = (-8 - 3)/(5- (-2)) = -11/7

2.) An equation of a line through (3,-2), (4, -2)  follows from previous solver:  y=-2 because the line is horizontal.

3.) Standard form for a line is Ax + By = C  for A and B not both zero.
first find the slope of x + 3y = 6,  rearranging it to y = (-1/3)x + 2
Slope is (-1/3) for given line.  The slope of a line perpendicular to this is 3, it is the negative reciprocal of (-1/3).

Next we have  y - 5 = 3* (x - (-3))

y - 5 = 3x + 9

3x -y = -14

Answer:  3x -y = -14